
Glass "H 14* 
Book. lCl^. 



Copyright^ . 



l^o<# 



COPYRIGHT DEPOSIT. 



WORKS OF 
PROF. R. C. CARPENTER 

PUBLISHED BY 

JOHN WILEY & SONS. 



Heating and Ventilating of Buildings. 

8vo, xv + 5^2 pages, 277 figures, cloth, $4.00. 

Experimental Engineering. 

For Engineers and for Students in Engineering 
Laboratories. 8vo, xix + 843 pages, 335 figures, 
cloth, $6.00. 



EXPERIMENTAL ENGINEERING 



AND 



MANUAL FOR TESTING. 



FOR ENGINEERS AND FOR STUDENTS IIV 
ENGINEERING LA BORA TORIES. 



BY 



ROLLA C. CARPENTER, M.S., C.E., M.M.E., 

PROFESSOR OF EXPERIMENTAL ENGINEERING, SIBLEY COLLEGE, 
CORNELL UNIVERSITY. 



SIXTH REVISED AND ENLARGED EDITION. 
FIRST THOUSAND. 



NEW YORK : 

JOHN WILEY & SONS. 

London: CHAPMAN & HALL, Limited* 

1906. 






V*> 



» 



LIBRARY of 0ON6RESS 

TwoGooles Received 

MAY 10 1906 

' COPY B. 



Copyright, 1892, 1906, 

BY 

ROLLA C. CARPENTER. 



£ 



x* 



P 



?v 



ROBERT DKUMMOND, ELECTROTYPER AND PRINTER, NEW YORK. 



i 



PREFACE TO THE SIXTH EDITION. 



The first edition of the present work, entitled " Notes to 
Mechanical Laboratory Practice," was published in 1890; a 
second edition was published in 1891, and soon exhausted by an 
unexpected demand from engineering schools and the profession. 
The two early editions were prepared especially for the use of 
students in the Laboratory of Experimental Engineering, Sibley 
College, Cornell University, for the purpose of facilitating in- 
vestigation of engineering subjects, and of providing a systematic 
course of instruction in experimental work. 

The book was rewritten and much enlarged in 1892, and the 
title changed to Experimental Engineering. Four revised editions, 
containing a total of nearly ten thousand volumes, have been 
published since that time, in which various errors in the previous 
editions have been eliminated and additions made as required 
by the advance in the engineering art. The present, or sixth, 
edition is a complete revision of the entire book, with a new 
index and more than 100 pages of additional matter, including 
chapters on the testing of the Steam-turbine, the Air-compressor, 
and the Refrigerating-machine. It also contains much new 
matter relating to the testing of the Gas-engine. 

Respecting the field of the book, attention is called to the 
well-known and universally acknowledged fact that nearly all 
the recent progress in the engineering art is due to experimental 
investigation and research. Without such research the coefficients 
which are employed in making practical application of theoretical 
laws would not have been known, and engineering constructions 



iv PREFACE TO THE SIXTH EDITION. 

and machines which are now designed with confidence to pro- 
duce definite results, in advance of actual trial, would not have 
been possible. Experimental research and test are also valuable 
in discriminating between correct and false theories, since it is 
true that any reliable theory will be verified by experiment, whereas 
no theory can be correct which does not accord with experimental 
results. 

On the other hand, experimental results may lead to erroneous 
conclusions if the fundamental rational theory which applies is 
unknown, and it is for this reason important to understand the 
fundamental theory, if any exist, in advance of the experimental 
work. The fact should be noted and appreciated that without 
theory all engineering knowledge would be reduced to a mere 
inventory of the results of observations. It is attempted in the 
work on Experimental Engineering to point out the relation 
between the fundamental theory and the experimental results 
where such a theory exists, and for other cases to point out general 
methods of drawing conclusions from the observations and data 
obtained in performing the experiments. 

The principal object of the present edition is to supply a text- 
book for laboratory use, but it is also believed that the volume will 
not be without value as a reference-book to the consulting and 
practising engineer, since it contains in a single volume the prin- 
cipal standard methods which have been from time to time adopted 
by various engineering societies for the testing of materials, engines, 
and machinery, and an extensive series of tables useful in com- 
puting results. It also contains a description of the apparatus 
required in testing, directions for taking data and deducing results 
in engineering experiments, as applied in nearly every branch of 

the art. 

The book is, however, intended chiefly for use in engineering 
laboratories, and presents information which the experience of 
the author has shown to be necessary to carry out experiments 
intelligently and without great loss of time on the part of students. 
For this purpose it gives a brief statement of the theoretical prin- 



PREFACE TO THE SIXTH EDITION. V 

ciples involved in connection with each experiment, with references 
to complete demonstrations, short descriptions of the various 
classes of engineering apparatus or machinery, a full statement 
of methods of testing and of preparing reports. For a few cases 
where references cannot readily be given, demonstrations of the 
fundamental principles are given in full. 

An attempt has been made, by dividing the book into several 
chapters of moderate length, by making the paragraphs short, 
and by placing the paragraph-numbers at the top of the page, 
to make references to the book easy to those who care to consult 
it. References which will, it is believed, be found ample for all 
purposes of the student or engineer are given, where needed, to 
more complete treatises on the various subjects discussed. 

The importance of an engineering laboratory is now so fully 
recognized in colleges of engineering that it is hardly necessary 
to refer to the advantages which it confers. If devoted to educa- 
tional purposes, it should afford students the opportunity of 
obtaining practical knowledge of the application and limitation 
of theoretical principles by personal investigation, under such 
direction as will insure systematic methods of observation, accurate 
use of apparatus, and the proper methods of drawing conclu- 
sions and of making reports. If of an advanced character, it 
should also provide facilities for systematic research by skilled 
observers, for. the purpose, among other things, of discovering 
laws or coefficients of value to the engineering profession. 

This work deals principally with the educational methods, 
the use of apparatus, and the preparation required for making 
a skilled observer. 

In an engineering laboratory for the education of students, 
a systematic schedule of experiments parallel to the course of 
instruction in theoretical principles is recommended. While such 
a laboratory course cannot be laid down here as applicable to all 
courses of instruction in engineering, the following schedule of 
studies is presented for consideration as one which has been 
successfully adopted in the instruction of large classes in Sibley 



VI PREFACE TO THE SIXTH EDITION. 

College. The order of the experiments was largely determined 
by the previous training of the men, and by the attempt to 
make a limited amount of apparatus do maximum duty. The 
schedule is presented more as an illustration of one that has 
been practically tested, and for which the work on Experimental 
Engineering is adapted, than as a model for other institutions 
to follow. 

COURSE OF EXPERIMENTS, 
SIBLEY COLLEGE ENGINEERING LABORATORY. 

Junior Year. 

First Term. 

Strength of Materials — Tensile and Transverse; Calibration — Indicator- 
springs and Steam-gauges; Weirs and Water-meters; Mercurial Thermom- 
eters; Pyrometers; Transmission-dynamometers; Slide-rule; Calculating- 
machines; Planimeters; Calorimeter and Indicator-practice. 

Second Term. 

Strength of Materials — Compression and Torsion; Lubricants — Viscosity; 
Flash-test; Coefficient of Friction; Steam-engine — Valve-setting; Flue -gas 
Analysis; Temperature — Pyrometers, Air- thermometers; Calibration — Indi- 
cator-springs; Efficiency-tests — Steam-boiler; Steam-pump; Steam-engine; 
Hydraulic Ram. 

Senior Year. 

First Term. 

Strength of Materials — Brick; Stone; Cement; Efficiency -tests — Hot-air 
Engine (2 tests) ; Gas-engine (3 tests) ; Injector; Centrifugal Pump; Hydrau- 
lic Motor; Belting; Steam Boiler; Compound Engine; Oil-engine (2 tests); 
DeLaval Steam Turbine; Parsons Steam Turbine. 

Second Term. 

Strength of Materials — Springs; Tension test on Emery -machine ; 
Efficiency -tests — Air-compressor; Triple -expansion Engine; University Elec- 
tric-lighting Plant; Doble Water-wheel; Pelton Wheel; Refrigeration; Com- 
pound and Triple-expansion Engine by Hirn's Method; Special Research; 
Thesis Work. 

The work required of each student per week is substantially 
as follows: one laboratory exercise three hours in length, one 



PREFACE TO THE SIXTH EDITION. Vll 

recitation one hour in length, and the computation of the data 
and the preparation of a report, including data, results, and all 
necessary curves. The report is required to be full and com- 
plete, and is expected to train the young man in methods of writing 
English and of reporting in his own language what he has learned 
respecting the subject under investigation in the laboratory and 
in the references, as well as to teach him method? of observing 
and recording the data and of computing the results of the test. 
For the purpose of performing the experiments the students are 
divided into groups of three, and the experiments are usually 
arranged as to require three observers or multiples thereof. The 
computation of results is made by all the members of the group, 
but each man is required to write an individual report of the test. 
The credit given is the same as for a recitation course requiring 
three hours per week. The student's work is performed under 
the personal direction of a competent instructor, who has charge 
usually of twelve to fourteen men, who gives such detailed instruc- 
tion as is required, and reads, corrects, and grades all reports. 
The student is required, whenever practicable or possible, to 
operate his own machine or apparatus during the test, in order 
to obtain practical skill in the handling and operation of appara- 
tus, machines, and prime movers, which is believed to meet an 
important requirement of an engineering laboratory. He is not 
expected to do the shop work required for construction of the 
apparatus, or that required for the preparation of the experi- 
ment, as the time at his command is not sufficient for such work; 
and besides, instruction in shop work is given in a different 
department in Sibley College. 

The full list of subjects treated in the book is given in the 
table of contents which immediately follows the preface. Some 
of the more important divisions of the work are as follows • 

Experimental Methods of Investigation. 

Reduction of Experimental Data Analytically and Graphically. 
Apparatus for Reduction of Experimental Data, including use of Slide-rule, 
Planimeter, etc. 



Vlll PREFACE TO THE SIXTH EDITION. 

Strength 01 Materials, including General Formulae, Description of Testing 

machines, and Methods of Testing. 
Cement-testing Machines and Methods of Testing. 
Machines and Methods for Testing Lubricants and Friction. 
Dynamometers and Machines for the Measurement of Power. 
Hydraulics, Hydraulic Machinery, and Methods of Testing. 
Measurement of Pressure and Temperature. 
Measurement of Moisture in Steam by Calorimeters. 
Fuel-calorimeters and Flue-gas Analysis. 
Tne Steam-engine and Methods of Testing. 
The Steam-boiler and Methods of Testing. 
The Steam-turbine and Methods of Testing. 
Gas and Hot-air Engines and Methods of Testing. 
The Injector and Methods of Testing. 
Methods of Testing Locomotives. 
Methods of Testing Pumping-engines. 
Air-compressors and Methods of Testing. 
Refrigerating-machines and Methods of Testing. 

The author has been assisted in the preparation of the various 
editions of the book by his colleagues and assistants in Sibley 
College, and is indebted to them for many suggestions and a 
great deal of valuable information. Ample credit is given authori- 
ties from whom information has been obtained in the body of the 
book in connection with the matter under discussion. In the 
early editions of the work the writer was under special obligation 
to the late Dr. R. H. Thurston and to Professor C. W. Scribner; 
for the later editions to Assistant Professor H. Diederichs, and 
C. Hirshfeldt, and to Mr. R. L. Shipman, Mr. W. M. Sawdon, 
and Mr. G. B. Upton. 



TABLE OF CONTENTS. 



INTRODUCTION. 

ARTICLE PAGE 

i. Objects of Engineering Experiment i 

2. Relation of Theory to Experiment 2 

3. The Method of Investigation * 2 

4. Classification of Experiments 3 

5. Efficiency-tests 3 



CHAPTER I. 

REDUCTION OF EXPERIMENTAL DATA. 

6. Classification of Errors 5 

7. Probability of Errors 6 

8. Errors of Simple Observations 7 

10. Combination of Errors 9 

12. Deduction of Empirical Formulae 10 

15. Rules and Formulas for Approximate Calculation 15 

16. Rejection of Doubtful Observations 17 

17. Errors to be Neglected 18 

18. Accuracy of Numerical Calculations 19 

19. Graphical Representation of Experiments 20 

21. Autographic Diagrams 21 

22. Construction of Diagrams 22 

CHAPTER II. 

APPARATUS FOR REDUCTION OF EXPERIMENTAL DATA. 

2^. The Slide-rule 24 

25. The Vernier 29 

26. The Polar Planimeter 30 

30. The Suspended Planimeter 41 

31. The Coffin Planimeter 41 

tx 



x TABLE OF CONTENTS. 

ARTICLE PAGE 

34. The Roller Planimeter 45 

36. Care and Adjustment of Planimeters 50 

37. Directions for Use of Planimeters 51 

38. Calibration of Planimeters 52 

39. Errors of Planimeters 55 

40. The Vernier Caliper 57 

41. The Micrometer 58 

42. The Micrometer Caliper 59 

43. The Cathetometer 62 

44. Computation Machines 64 



CHAPTER III. 

STRENGTH OF MATERIALS — GENERAL FORMULAE. 

45. Definitions 67 

46. Strain-diagrams 69 

47. Viscosity 70 

48. Notation 72 

49. Tension 72 

51. Compression 73 

52. Transverse 76 

54. Shearing and Torsion 81 

55. Modulus of Rigidity 83 

58. Combination of Two Stresses 84 

60. Thermodynamic Relations 86 



CHAPTER IV. 



STRENGTH OF MATERIALS — TESTING-MACHINES. 



6l. 
65. 

66. 

68. 
70. 

73- 

75- 
76. 

77- 



General Description of Machines 88 

Shackles or Holders 98 

Emery Testing-machine 100 

Riehle Bros.' Testing-machine 107 

Olsen Testing-machine no 

Thurston's Torsion Machines 114 

Riehle's and Olsen's Torsion Machines 118 

Impact Testing-machine 119 

Cement-testing Machines 119 

Testing-machine Accessories 124 



TABLE OF CONTENTS. xi 

ARTICLE PAGE 

78 to 86. Extensometers 124 

87. Deflectometer 135 

CHAPTER V. 

METHODS OF TESTING MATERIALS OF CONSTRUCTION. 

88. Form of Test-pieces . 136 

93. Elongation — Fracture. 143 

94. Strain-diagrams 144 

95. Tension Tests 145 

99. Compression Tests 154 

100. Transverse Tests 155 

102. Elastic Curve 159 

103. Torsion Test 160 

105. Impact Test 163 

107. Special Tests of Materials 165 

109. Method of Testing Bridge Materials 168 

1 10. Admiralty Tests 172 

in. Lloyd's Tests for Steel used in Ship-building 173 

112. Tests for Cast-iron Water-pipe 174 

114. Testing Stones 175 

115. " Bricks 178 

116. ' ' Paving Material 179 

117. ' * Hydraulic Cements 181 



122 
127 
128 
129 
130 

*3i 
136 

143 

144 

147 
151 
152 



CHAPTER VI. 

FRICTION— TESTING OF LUBRICANTS. 

Friction — Definitions — Useful Formulae 196 

Friction of Teeth 199 

" " Cords or Belts . 199 

" Fluids 200 

' ' ' ' Lubricated Surfaces 201 

Testing of Lubricants — Density 201 

' ' " " Viscosity 2C9 

' ' " Gumming 210 

" " " Flash-test 210 

Testing of Lubricants — Cold Test 213 

Oil-testing Machines— Rankine's 215 

Thurston's 217 



Xll TABLE OF CONTENTS. 

ARTICLE p AGE 

155. Coefficient of Friction 222 

157. Riehle's Oil-testing Machine 224 

158. Durability Test of Lubricants . . 226 

159. Ashcroft's Oil-testing Machine 227 

160. Boult's " " 227 

162. Experiment with Limited Feed 231 

163. Forms for Report of Lubricant Test 233 



CHAPTER VII. 

MEASUREMENT OF POWER — BELT-TESTING. 

165. Absorption Dynamometer. The Prony Erake 235 

173. " " " Alden Brake 241 

178. Practical Directions for Use of Brake 244 

179. Pump-brakes 245 

180. Fan-brakes 245 

181. Traction Dynamometers 246 

182. Transmission Dynamometers — Morin 247 

186. 
187. 
188. 
189. 
192. 
194. 
195- 



Steelyard 250 

Pillow-block 252 

Lewis 252 

Differential 255 

Emerson 259 

Van Winkle. 261 

Belt 263 

197. Belt-testing Machine, with Directions 264 

CHAPTER VIII. 

MEASUREMENTS OF LIQUIDS AND GASES. 

200. Theory of the Flow of Water 270 

201. Flow of Water over Weirs — Formulae 272 

203. " " " through Nozzles — Formulae 275 

205. " ' ' " under Pressure — Formulae 276 

206. ' { * ' " in Circular Pipes 277 

207. " " " through a Diaphragm — Formulae 279 

209. Method of Measuring the Flow of Water by Weirs 281 

213. " " " " " " " " Meters 283 

217. " " tl " " il " "Nozzles 287 

219. " " " " " " " "Diaphragms 288 

220. " " " " " li " "inStreams 289 

222. " " " " " " " " Pitot'sTube 292 



TABLE OF CONTENTS. xni 

ARTICLE PAGE 

225. Flow of Compressible Fluids through an Orifice. 295 

229. " " " " in a Pipe 299 

230. " " Steam , , 300 

232. Gas-meters 304 

2^. Anemometer 306 



CHAPTER IX. 

HYDRAULIC MACHINERY. 

235. Classification 308 

239. Water-pressure Engines. ........ 1 309 

241. Overshot Water-wheels 311 

242. Breast-wheels 313 

243. Undershot Wheels 313 

244. Impulse -wheels. . . . 314 

245. Turbine 315 

248. Reaction -wheels 317 

249. The Hydraulic Ram 321 

250. Methods of Testing Water-motors 322 

253. Pumps 327 

256. Test of Pumps 330 

258. Form for Data and Report of Pump-test 332 



CHAPTER X. 

DEFINITIONS OF THERMODYNAMIC TERMS. 

259. Books of Reference 325 

260. Units of Pressure 336 

261. Heat and Temperature 337 

264. Properties of Steam 340 

267. Steam-tables 344 

CHAPTER XL 

MEASUREMENT OF PRESSURE. 

268. Manometers 345 

271. Mercury Columns 349 

273. Draught-gauges 351 



Xiv TABLE OF CONTENTS. 

ARTICLE PAGE 

277. Steam-gauges 357 

281. Apparatus for Testing Gauges 363 



CHAPTER XII. 

MEASUREMENT OF TEMPERATURE. 

285. Mercurial Thermometers 369 

288. Air-thermometers 37! 

295. Calibration of Thermometers 380 

296. Metallic Pyrometers 380 

298. Air and Calorimetric Pyrometers 381 

299. Determination of Specific Heat 382 

302. Electric Pyrometers 385 

303. Optical Pyrometers , . . 386 



CHAPTER XIII. 

METHODS OF MEASURING MOISTURE IN STEAM. 

305. Definitions 390 

307. General Methods 391 

314. Errors in Calorimeters 396 

315. Sampling the Steam 399 

317. Water Equivalent of Calorimeter .".... 401 

318. Barrel Calorimeter 402 

321. Hoadley Calorimeter 407 

323. Barrus Continuous Calorimeter 411 

326. ' ' Superheating " 416 

328. Throttling Calorimeter.^ 418 

336. Separator " 430 

341. Chemical " 440 

CHAPTER XIV. 

HEATING VALUE OF COALS — FLUE -GAS ANALYSIS. 

343. Combustion — Definition and Table 443 

344. Heat of Combustion 444 

345. Determination of Heat by Welter's Law 446 

346. Temperature produced by Combustion 448 



TABLE OF CONTENTS. 



347. Composition of Fuels 450 

348. Fuel-calorimeters — Principle 451 

352. " Favre and Silbermann's 453 

353- Thompson's 455 

354- Berthkr. 456 

355. ' ' Berthelot Bomb 459 

35 6 - Carpenter 463 

357. Value of Fuel by Boiler-trial 472 

358. Analysis of the Products of Combustion 473 

360. Reagents for Flue -gas Analysis 475 

363. Elliot's Flue-gas Apparatus 479 

364. Wilson's " " 481 

365. Orsat's " " 481 

366. Hemple's " " 483 

367. Deductions from Flue-gas Analysis 486 



CHAPTER XV. 

METHOD OF TESTING STEAM-BOILERS. 

369. Objects of Eoiler-testing 492 

371. Efficiency of a Eoiler 493 

375. Standard Method of Testing Steam-boilers 495 

377. Concise Directions for Testing Boilers 513 



CHAPTER XVI. 

THE STEAM-ENGINE INDICATOR. 

378. Uses of the Indicator 515 

380. Early Forms 517 

381. Richards 518 

382. Thompson 519 

383. Tabor 520 

384. Crosby 521 

385. Indicators with External Springs 523 

387. Optical Indicators 525 

390. Reducing-motions 529 

393. Calibration 535 

397. Method of Attaching to the Cylinder 543 

398. Directions for Use 545 



XVI TABLE OF CONTENTS. 



CHAPTER XVII. 

THE INDICATOR-DIAGRAM. 

ARTICLE PAGE 

400. Definitions 547 

401. Measurement of Diagrams 551 

403. Form of Diagram 553 

4C6. Weight of Steam from the Diagram 557 

407. Clearance from the Diagram 560 

408. Cylinder-condensation and Re-evaporation 561 

409. Discussion of Diagrams 562 

410. Diagrams from Compound Engines 565 

411. Crank -shaft and Steam-chest Diagrams 567 



CHAPTER XVIII. 

METHODS OP TESTING THE STEAM-ENGINE. 

412. Engine Standards 569 

414. Measurement of Speed 571 

417. Surface Condenser 576 

418. Calibration of Apparatus 578 

419. Preparations for Testing 581 

421. Quantities to be Observed 583 

422. Preliminary Indicator-practice 584 

423. Valve-setting 586 

424. Friction-test 589 

425. Efficiency-test 589 

426. Hirn's Analysis 590 

430. " " of Compound Engines , 603 



CHAPTER XIX. 

PUMPING-ENGINES AND LOCOMOTIVES. 

433. Standard Method of Testing Pumping-engines 614 

434. ' ' ' ' " " Locomotives 634 

435. Experimental Engines. 656 



TABLE OF CONTENTS. xvn 



CHAPTER XX. 



EXPERIMENTAL DETERMINATION OF INERTIA. 

ARTICLE PAGE 

436. General Effects of Inertia 660 

437. The Williams Inertia-indicator. . . . 661 

438. ' ' Inertia -diagram e 664 



CHAPTER XXI. 

THE INJECTOR AND PULSOMETER. 

439. Description of the Injector. 670 

440. Theory 672 

442. Limits of 676 

443-5. Directions for Testing 679 

446-7. The Pulsometer 683 

CHAPTER XXII. 

THE STEAM-TURBINE. 

448. General Principles < 686 

449. Impulse Type (De Laval) 687 

450. Reaction Type (Parsons). 689 

451. Combined Type (Curtis) 690 

452. Testing 691 

CHAPTER XXIII. 

HOT-AIR AND GAS ENGINES. 

454. General Principles 692 

455. Ericsson Hot-air Engine 692 

456. Rider Hot-air Engine. 693 

457. Theory 695 

458. Method of Testing 095 

460. The Gas-engine 701 

461. Oil-engines 709 

462. Theoretical Formulae. 711 

463. Cycle of Operation 713 



TABLE OF CONTENTS. 



ARTICLE 



PAGE 



464. Method of Testing 7I4 

465. Data and Results of Test 7x7 



CHAPTER XXIV. 

AIR-COMPRESSORS. 

466. Types of Compressors 720 

467. Piston Air-compressor 720 

468. Rotary Blowers 723 

469. Centrifugal Fans 724 

470. Measurement of Pressure and Velocity 725 

471. Clearance, Effect of 728 

472. Loss of Work Due to Rise of Temperature 728 

473. Centrifugal Fan, Theory of 729 

474. Test of Air-compressor Data Sheets 730 

475. * ' ' ' Centrifugal Elower 733 

CHAPTER XXV. 

MECHANICAL REFRIGERATION. 

476. Systems of Mechanical Refrigeration 734 

477. Relation of. Work to Heat Transfer 735 

478. Working Fluids, Properties of 736 

479. Efficiency of the Refrigerating -machine 738 

480. Heat Losses 740 

481. The Air-refrigerating Machine 741 

482. The Ammonia Refrigerating -machine 742 

483. Relations of Pressure and Volume 744 

484. Absorption System of Refrigeration 747 

Logs and Data Sheets 749 



CHAPTER XXVI. 

PRACTICAL TABLES. 
TABLE 

I. U. S. Standard and Metric Measures 754 

II. Numerical Constants -. 756 

III. Logarithms of Numbers 769 

IV. Logarithmic Functions of Angles 771 



TABLE OF CONTENTS, 



xix 



TABLE PAGE 

V. Natural Functions of Ang.es 777 

VI. Coefficients of Strength of Materials 781 

VII. Strength of Metals at Different Temperatures 782 

VIII. Important Properties of Familiar Substances 783 

IX. Coefficient of Friction 784 

X. Hyperbolic Naperian Logarithms 784 

XL Moisture Absorbed by Air 785 

XII. Relative Humidity of the Air 785 

XIII. Table for Reducing Beaume's Scale-reading to Specific Gravity 786 

XIV. Composition of Fuels of U. S 787 

XV. Buel's Steam-tables 788 

XVI. Entropy of Water and Steam 794 

XVII. Discharge of Steam: Napier Formula 795 

XVIII. Water in Steam by Throttling Calorimeter 795 

Diagram for Determining Per Cent of Moisture in Steam 796 

XIX. Factors of Evaporation 797 

XX. Dimensions of Wrought-iron Pipe 798 

XXI. Density and Weight of Water per Cubic Foot 799 

XXII. Horse -power per Pound Mean Pressure. . 800 

XXIII. Water Rate Computation Table for Engines 801 

XXIV. Weirs with End Contraction 803 

XXV. Weirs without End Contraction 803 

XXVI. Horse-power of Shafting 804 

XXVII. " " Belting 804 

Sample-sheet of Cross-section Paper 805 

IMPORTANT TABLES IN BODY OF BOOK. 

Moments of Inertia 78 

Units of Pressure Compared 336 

Thermometric Scales 337 

Melting-points and Specific Heats of Metals 383 

Maximum Temperature of Combustion. . 450 

Average Composition of Fuels 451 

Properties of Saturated Ammonia 738 



INTRODUCTION. 



I. Objects of Engineering Experiments. — The object of 

experimental work in an engineering course of study may be 
stated under the following heads : firstly, to afford a practical 
illustration of the principles advanced in the class-room ; sec- 
ondly, to become familiar with the methods of testing; thirdly, 
to ascertain the constants and coefficients needed in engineer- 
ing practice ; fourthly, to obtain experience in the use of vari- 
ous types of engines and machines , fifthly, to ascertain the 
efficiency of these various engines or machines ; sixthly, to de- 
duce general laws of action of mechanical forces or resistances, 
from the effects or results as shown in the various tests made. 
The especial object for which the experiment is performed 
should be clearly perceived in the outset, and such a method 
of testing should be adopted as will give the required informa- 
tion. 

This experimental work differs from that in the physical 
laboratory in its subject-matter and in its application, but the 
methods of investigation are to a great extent similar. In per- 
forming engineering experiments one will be occupied princi- 
pally in finding coefficients relating to strength of materials or 
efficiency of machines ; these, from the very nature of the ma- 
terial investigated, cannot have a constant value which will be 
exactly repeated in each experiment, even provided no error 
be made. The object will then be to find average values of 
these coefficients, to obtain the variation in each specific test 



2 EXPERIMENTAL ENGINEERING. [§ 3- 

from these average values, and, if possible, to find the law and 
cause of such variation. 

The results are usually a series of single observations on a 
variable quantity, and not a series of observations on a con- 
stant quantity; so that the method of finding the probable 
error, by the method of least squares, is not often applicable. 
This method of reducing and correcting observations is, how- 
ever, of such value when it is applicable, that it should be 
familiar to engineers, and should be applied whenever practi- 
cable. The fact that single observations are all that often can 
be secured renders it necessary in this work to take more than 
ordinary precautions that such observations be made correctly 
and with accurate instruments. 

2. Relation of Theory to Experiment. — It will be found 
in general better to understand the theoretical laws, as given 
in text-books, relating to the material or machine under inves- 
tigation, before the test is commenced ; but in many cases this 
is not possible, and the experiment must precede a study of the 
theory. 

It requires much skill and experience in order to deduce 
general laws from special investigations, and there is always 
reason to doubt the validity of conclusions obtained from such 
investigations if any circumstances are contradictory, or if any 
cases remain unexamined. 

On the other hand, theoretical deductions or laws must be 
rejected as erroneous if they indicate results which are con- 
iradictory to those obtained by experiments subject to condi- 
tions applicable in both cases. 

3. The Method of Investigation is to be considered as 
consisting of three steps : firstly, to standardize or calibrate the 
apparatus or instruments used in the test ; secondly, to make 
the test in such a way as to obtain the desired information ; 
thirdly, to write a report of the test, which is to include a full 
description of the methods of calibration and of the results, 
which in many cases should be expressed graphically. 

The methods of standardizing or calibrating will in gen- 
eral consist of a comparison with standard apparatus, under 



§5-] INTRODUCTION. ' 3 

conditions as nearly as possible the same as those in actual prac- 
tice. These methods later will be given in detail. The manner 
of performing the test will depend entirely on the experiment. 

The report should be written in books or on paper of a pre- 
scribed form, and should describe clearly: (i) Object of the 
experiment; (2) Deduction of formulas and method of perform- 
ing the experiment; (3) Description of apparatus used, with 
methods of calibrating; (4) Log* of results, which must include 
all the figures taken in the various observations of the calibra- 
tion as well as in the experiment. These results should be 
arranged, whenever possible, in tabular form; (5) Results of 
the experiment; these should be expressed numerically and 
graphically, as explained later; (6) Conclusions deduced from 
the experiment, and comparison of the results with those given 
by theory or other experiments. 

4. Classification of Experiments. — The method of per- 
forming an experiment must depend largely on the special object 
of the test, which should in every case be clearly comprehended. 
The following subjects are considered in this treatise, under 
various heads: (1) The calibration of apparatus; (2) Tests of 
the strength of materials; (3) Measurements of liquids and 
gases; (4) Tests of friction and lubrication; (5) Emciency- 
tests, which relate to (a) belting and machinery of transmission, 
(b) water-wheels, pumps, and hydraulic motors, (c) hot-air and 
gas engines, (d) air-compressors and compressed-air machinery, 
(e) steam-engines, boilers, injectors, and direct-acting pumps. 

5. Efficiency-tests. — Tests may be made for various ob- 
jects, the most important being probably that of determining the 
efficiency, capacity, or strength. 

The efficiency of a machine is the ratio of the useful work 
delivered by the machine to the wfyole work supplied or to the 
whole energy received. The limit to the efficiency of a machine 
is unity, which denotes the efficiency of a perfect machine. 

The whole work performed in driving a machine is evidently 
equal to the useful work, plus the work lost in friction, dissi- 
pated in heat, etc. The lost work of a machine often consists 



4 EXPERIMENTAL ENGINEERING. [§ 5- 

of a constant part, and in addition a part bearing some definite 
proportion to the useful work; in some cases all the lost work 
is constant. 

Efficiency -tests are made to determine the ratio of useful 
work performed to total energy received, and require the deter- 
mination of, first, the work or energy received by the machine; 
second, the useful work delivered by the machine. The friction 
and other lost work is the difference between the total energy 
supplied and the useful work delivered. In case the efficiency 
of the various parts of the machine is computed separately, the 
efficiency of the whole machine is equal to the product of the 
efficiencies of the various component parts which transmit energy 
from the driving-point to the working-point. 

The work done or energy transmitted is usually expressed 
in foot-pounds per minute of time, or in horse-power, which is 
equivalent to 33,000 foot-pounds per minute, or 550 foot-pounds 
per second of time. 



EXPERIMENTAL ENGINEERING, 



REDUCTION OF EXPERIMENTAL DATA. 

METHOD OF LEAST SQUARES— NUMERICAL CALCULATIONS- 
GRAPHICAL REPRESENTATION OF EXPERIMEN1 >. 



CHAPTER I. 
APPLICATION OF THE METHOD OF LEAST SQUARES. 

In the following articles the application of this method to 
reducing observations and producing equations from experi- 
mental data is quite* fully set forth. The theory of the 
Method of Least Squares is not given, but it can be fully 
studied in the work by Chauvenet published by Lippincott & 
Co., or in the work by Merriman published by John Wiley & 
Sons. 

6. Classification of Errors. — The errors to which all ob- 
servations are subject are of two classes: systematic and acci- 
dental. 

Systematic errors are those which affect the same quanti- 
ties in the same way, and may be further classified as instru- 
mental and personal. The instrumental errors are due to 
imperfection of the instruments employed, and are detected by 
comparison with standard instruments or by special methods 
of calibration. Personal errors are due to a peculiar habit of 
the observer tending to make his readings preponderate in 
a certain direction, and are to be ascertained by comparison of 

5 



6 EXPERIMENTAL ENGINEERING. [§ 7« 

observations: first, with those taken automatically; second, 
with those taken by a large number of observers equally skilled ; 
third, with those taken by an observer whose personal" error is 
known. Systematic errors should be investigated first of all, 
and their effects eliminated. 

A ccidental errors are those whose presence cannot be fore- 
seen nor prevented; they may be due to a multiplicity of causes, 
but it is found, if the number of observations be sufficiently 
great, that their occurrence can be predicted by the law of 
probability, and the probable value of these errors can be com- 
puted by the METHOD OF LEAST SQUARES. 

Before making application of the " Method of Least 
Squares," determine the value of the systematic errors, elimi- 
nate them, and apply the method of least squares to the de- 
termination of accidental errors. 

7. Probability of Errors. — The following* propositions are 
regarded as axioms, and are the fundamental theorems on 
which the Method of Least Squares is based : 

1st. Small errors will be more frequent than large ones. 

2d. Errors of excess and deficiency (that is, results greater 
or less than the true value) are equally probable and will be 
equally numerous. 

3d. Large errors, beyond a certain magnitude, do not occur. 
That is, the probability of a very large error is zero. 

From these it is seen that the probability of an error is a 
function of the magnitude of the error. Thus let x represent 
any error and y its probability, then 

By combination of the principles relating to the probability 
of any event Gauss determined that 

y = ce~** t ....... (i) 

in which c and h are constants, and e the base of the Napierian 
system of logarithms. 



§ 9-] APPLICATION OF METHOD OF LEAST SQUARES. 7 

8. Errors of Simple Observations. — It can be shown by 
calculation that the most probable value of a series of obser- 
vations made on the same quantity is the arithmetical mean, and 
if the observations were infinite in number the mean value would 
be the true value. The residual is the difference between any 
observation and the mean of all the Observations. The mean 
error of a single observation is the square root of the sum of the 
squares of the residuals, divided by one less than the number 
of observations. The probable error is 0.6745 time the mean 
error. The error of the result is that of a single observation 
divided by the square root of their number. 

Thus let 11 represent the number of observations, 5 the sum 
of the squares of the residuals; let e, e x , e if etc., represent the 
residual, which is the difference between any observation and 
the mean value ' let 2 denote the sum of the quantities indi- 
cated by the symbol directly following. 

Then we shall have 



Mean error of a single observation ± \/ . 

Probable error of a single observation ± 0.6745 a / , 

Mean error of the result ± a / -7 r. . (4) 

y n(n — 1) w 



(2) 
(3) 



y n(n- 



Probable error of the result ± 0.6745 a / . _ -r. (5) 

In every case 5 = -2V*. 

9. Example. — The following example illustrates the method 
of correcting observations made on a single quantity : 

A great number of measurements have been made to 
determine the relation of the British standard yard to the 



8 



EXPERIMENTAL ENGINEERING. 



B* 



meter. The British standard of length is the distance, on a 
bar of Bailey's bronze, between two lines drawn on plugs at 
the bottom of wells sunk to half the depth of the bar. The 
marks are one inch from each end. The measure is standard 
at J2° Fah., and is known as the Imperial Standard Yard. 

The meter is the distance between the ends of a bar of 
platinum, the bar being at o° Centigrade, and is known as the 
Metre des Archives. 

The following are some of these determinations. That 
made by Clarke in 1866 is most generally recognized as of 
the greatest weight. 



COMPARISON OF BRITISH AND FRENCH MEASURES. 



Name of Observer. 


Date. 


Observed 

length of meter 

in inches. 


Difference from 

the mean. 

Residual = e. 


Square of the 

Residuals. 

* 2 . 


Kater 


1821 
1832 
1866 

1884 
1885 


39.37079 

39-38I03 

39.370432 

39-370I5 

39-36985 


— O.OOI460 
+ 8780 

— 1818 

— 2IOO 

— O.OO2400 


0.000002 13 16 
O.OOOO770884 
O.OOOOO33124 
O.OOOOO44100 
O.OOOOO57600 




Clarke 






Mean value 




39.372250 




O.OOOO907024 





2e* = S = 0.0000907024, n = 5, n{n — 1) = 20. 



Mean error of a single observation 






00476. 



Probable error of single observation = ± 0.003 17. 



Mean error of mean value = ± \ / -7- — -x = 0.00213, 



Probable error of mean value 



= ± 0.00142. 



§11.] APPLICATION OF METHOD OF LEAST SQUARES. 9 

That is, considering the observations of equal weight, it 
would be an even chance whether the error of a single obser- 
vation were greater or less than 0.00317 inch, and the error 
of the mean greater or less than 0.00142. 

10. Combination of Errors. — When several quantities are 
involved it is often necessary to consider how the errors made 
upon the different quantities will affect the result. 

Since the error is a small quantity with reference to the re- 
sult, we can get sufficient accuracy with approximate formulae. 

Thus let X equal the calculated or observed result, F the 
error made in the result ; let x equal one of the observed 
quantities, and f its error. Then will 

F = ff x • ....... (6) 

in which -7— is the partial derivative of the result with respect 

to the quantity supposed to vary. In case of two quantities 
in which the errors are F, F f , etc., the probable error of the 
result 



= ± VF 2 + F n (7) 

II. As an example, discuss the effect of errors in counting the 
number of revolutions, and in measurement of the mean effec- 
tive pressure, acting on the piston, with regard to the power 
furnished by a steam-engine. Denote the number of revolu- 
tions by n, the mean pressure by p, the length of stroke in feet 
by /, and the area of piston in square inches by a ; the work 
in foot-pounds done on one side of the piston by W. Then 

W — plan, F = lanf y 

F dW , _, 

-j. = —j— = lan y b =.plaf\ 

J d P 

F' dW ■ 
7 = ~dn =? la ' 



IO EXPERIMENTAL ENGINEERING. [§ 12. 

The error/ in the mean pressure is itself a complicated 
one, since p is measured from an indicator-diagram and depends 
on accuracy of the indicator-springs, accuracy of the indicator- 
motion, and the correct measurement of the indicator-diagram. 
These errors vary with different conditions. Suppose, however, 
the whole error to be that of measurement of the indicator- 
diagram. This is usually measured with a polar planimeter, of 
which the minimum error of measurement may be taken as 
0.02 square inch ; with an indicator-diagram three inches in 
length this corresponds to an error of 0.0067 of an inch in ordi- 
nate. In a similar manner the error in the number of revolu- 
tions depends on the method of counting: with a hand-counter 
the best results by an expert probably would involve an error 
of one tenth of a second ; with an attached chronograph the 
error would be less, and would probably depend on the accu- 
racy with which the results could be read from the chronograph- 
diagram. The ordinary errors are fully three times those 
given here. 

Take as a numerical example, a = 100 square inches, 
1 = 2 feet, n = 300, / = 50 pounds, /= 0.335, /' = 0.5. 

F = 20,100, F = 5,000, W = 3,000,000. 



Probable error = ± VF' Z + F* = 20,712 ft.-lbs., which in this 
case is 0.0069 of the work done. 

12. Deduction of Empirical Formulae. — Observations are 
frequently made to determine general laws which govern 
phenomena, and in such cases it is important to determine 
what formula will express with least error the relation between 
the observed quantities. 

These results are empirical so long as they express the re- 
lation between the observed quantities only; but in many cases 
they are applicable to all phenomena of the same class, in 
which case they express engineering or physical laws. 

In all these cases it is important that the form of the equa- 
tion be known, as will appear from the examples to be given 
later. The form of the equation is often known from the 



§ 1 3-] APPLICATION OF METHOD OF LEAST SQUARES. II 

general physical laws applying to similar cases, or it may be 
determined by an inspection of the curve obtained by a 
graphical representation of the experiment. A very large class 
of phenomena may be represented by the equation 

y = a + Bx + Cx 1 + Dx 3 + etc (8) 

In case the graphical representation of the curve indicates a 
parabolic form, or one in which the curve approaches parallel- 
ism with the axis of X, the empirical formula will probably be 
of the form 

y = A + £x* + Cx* + Dx*-\-etc. ... (9) 

In case the observations show that, with increasing values of x, 
;/ passes through repeating cycles, as in the case of a pendulum, 
or the backward and forward motion of an engine, the charac- 
teristic curve would be a sinuous line with repeated changes 
in the direction of 'curvature from convex to concave^ The 
equation would be of the form 



y^A + B.sin l —x + £ 2 cos ^—x + C x sin ^-2X 
m mm 

+ C a cos - — -2x + etc. . . . (10) 
m 



Still another form which is occasionally used is 

y = A -f- B sin mx -f- C sin 2 mx -\- etc. . . (1 1) 

13. General Methods. — A method of deducing the em- 
pirical formula is illustrated by the following general case : 

In a series of observations or experiments let us suppose 
that the errors (residuals) committed are denoted by e, £' ', e" 9 



12 EXPERIMENTAL ENGINEERING. |_§ J 3* 

etc., and suppose that by means of the observations we have 
deduced the general equations of conditions as follows: 

e = h -f- ax -\- by -\- cz, 
e' =h' \-a'x + b f y + c'z, I 
e" = h" + a"x + b"y + c"z, \ 
e »> - h"' + a'"x + *"> + *"'*, | 
etc. etc. etc. J 

Let it be required to find such values of x, y, z, etc., that the 
values of the residuals e, e\ e" y e'" , etc., shall be the least pos- 
sible, with reference to all the observations. 

If we square both members of each equation in the above 
group and add them together, member to member, we shall 
have 

f _|_ e " _[- e ' n + e" n + etc. = x\a 2 + a /2 + a"* + etc.) 

+ 2x\{ah + a'h' + a"h" + etc.)+ a{py +cz + etc.) 
+ a\b'y + c'z + etc.) + etc. \ + h 2 + h' 2 + etc. 

This equation may be arranged with reference to x as 
follows : 

u = e * + ^' 2 + ?" 2 + etc. = Px 2 + 20* + ^ + etc. ; 

in which the various coefficients of the different powers of x 
are denoted by the symbols P, Q, R, etc. 

Now in order that these various errors may be a minimum, 
^ 2 _j_ e n _|_ e "* _j_ etc. = u must be a minimum, in which case 
its partial derivative, taken with respect to each variable in 
succession, should be separately equal to zero. Hence 

or, substituting the values of P and Q, 

x(a 2 + a' 2 + etc.) + aA + ah' + etc. -\- a (ty + cz + etc.) 

+ a '(£> + ^ + etc.) + etc. = O. 

Similar equations are to be formed for each variable. 



§ 1 4.] APPLICATION OF METHOD OF LEAST SQUARES. 1 3 

From the form of these equations we deduce the principle 
that in order to find an equation of condition- for the minimum 
error with respect to one of the unknown quantities, as x for 
example, we have simply to multiply the second member of each 
of the equations of condition by the coefficient of the unknown 
quantity in that equation, take the sum of the products, and place 
the result equal to zero. Proceed in this manner for each of the 
unknown quantities, and there will result as many equations as 
there are unknown quantities, from which the required values 
of the unknown quantities may be found by the ordinary 
methods of solving equations. 

14. Example. — As an illustration, suppose that we require 
the equation of condition which shall express the relation be- 
tween the number of revolutions and the pressure expressed 
in inches of water, of a pressure-blower delivering air into a 
closed pipe. Let m represent the reading of the water-column, 
and n the corresponding number of revolutions. Suppose 
that the observations give 

for m = 24 inches, n = 297 revolutions • 
" m = 32 " n — 340 " 

" m = 33 " » = 355 

" m = 35 " n = 376 " 

Average values for m = 31 inches, n = 342 revolutions. 
Arranging the results in the following form, we have : 



Water-column. 


Revolutions. 


Observations. 


Residuals. 


Observations. 


Residuals. 


24 

32 
33 
35 


-7 

+ 2 

+ 4 


297 
340 
355 
376 


-45 

— 2 

+ 13 

+ 34 



Assume that the equation of condition is of the form 

A+Bx+Cx 2 =y. 



14 



EXPERIMENTAL ENGINEERING. 



[§1 + 



To find those values of A, B, and C which will most 
nearly satisfy the equation, as shown in the experiment: 
Taking the values of x, as the residual or difference between 
the mean and any observation in height of water-column, and 
the value of y as the corresponding residual in number of 
revolutions, we have the following equations of condition : 

A - 7 B + 4 gC= -45, j 
A + £+ C=- 2, I 
A + 2B+ 4 C= + i 3 , J * 
A+4B+i6C=+ 34 .) 

Multiplying each equation by the coefficient of A in that 
equation, we have 



A -yB + 4gC= -45, 
A+ B + C= - 2, 
A + 2B+ 4 C= + i 3 , 
A + 4 B+i6C= + 3 4 . 



Equations of minimum condi- 
tion of error with respect to A. 



4 A -\-0B-\-j0C = O. III. Sum of equations in group II. 

Multiplying each equation in group I by the coefficient of 
B in that equation, we have 

-7^+49^-343^= 315 ~ 
A + B + C=- 2 
2A+ 4 B+ SC= 26 
4^ + 16^ + 6 4 C= 136 



Equations of minimum 
IV. condition of error with 
respect to B. 



oA -f- yoB — 270C = 475 Sum of equations in group IV. 

Multiplying each equation in group I by the coefficient of 
C in that equation, we have 



49^ — 343^ + 2401 C — — 2205 

A+ B+ C=- 2 

4^+ SB+ i6C= 52 

\6A-\- 64^?+ 2566^= 544 



Equations of minimum 
V. condition of error with 
respect to C. 



JoA — 26SB + 2674C = — 161 1 Sum of equations in group V. 



§ 1 5-] APPLICATION OF METHOD OF LEAST SQUARES. 1 5 

The sums of these various equations of minimum condition are 
the same in number as the unknown quantities, and by com- 
bining them the various values of A, B, C, etc., can be deter- 
mined. We have, in the following case : 

4A + oB + yoC = o \ 

oA + 70B — 270C = 475 v VI. 
70^ — 268^ + 2674(7 = — 1611) 

Solving the above, 

A = 1.608 ; B = 7.140 ; C = — 0.0919. 

Substituting in the original equation of condition, 

y — 1.608 -j- 7.140^ — 0.0919^. 

To reduce this form to an equation expressing the probable 
relation of the number of revolutions to the height of the water- 
column, we must substitute for y its value, n — 342 ; and for x 
its value, m — 31. In this case we shall have 

m — 342 = 1.608 + 7.i4(w — 31) — 0.09 I9(w — 3i) a ; 

which reduced gives the following equation as the most proba- 
ble value in accordance with the observations : 

n = 34.952 -\- 13.02/^ — 0.0919*0"; 

which is the empirical equation sought. 

15. Rules and Formulae for Approximate Calculation.— 

When in a mathematical expression some numbers occur which 
are very small with respect to certain other numbers, and which 
are therefore reckoned as corrections, they may often be ex 
pressed with sufficient accuracy by an approximate formula, 
which will largely reduce the labor of computation. 



i6 



EXPERIMENTAL ENGINEERING. 



[§15. 



On the principle that the higher powers of very small quan- 
tities may be neglected with reference to the numbers them- 
selves, we can form a series by expansion by the binomial 
formula, or by division, in which, if we neglect the higher 
powers of the smaller quantities, the resulting formulae become 
much more simple, and are usually of sufficient accuracy. 

Thus, for instance, let d equal a very small fraction ; then 
the expression 



(a + S) m = a m + ma m - 1 d + 



VI- 



(m — 1) 



etc., 



will become a m + ma m ~ 1 S, if the higher powers of d be neglected. 
If d is equal to 10 1 00 part of a, the error which results from 
omitting the remaining terms of the series becomes very 
small, as in this case the value of d 2 = 100 ^ 000 fl. 



000000' 

The following table of approximate formulae presents several 
cases which can often be applied with the effect of materially 
reducing the work of computation, without any sensible effect 
on the accuracy: 



(1 + d) m = 1 + mS t 
(I + d) 2 = 1 + 2d, 



i/T+d = i+id, 
(1 + d) 3 =i+3*, 
= 1 - d, 



i + d 
1 

1 

4/T+d 



= I — 2d, 
= !■-**, 



(I- 


- 6) m 


= I — md ; 


(I- 


- d) 2 


= I — 2d; 


Vi 


— d 


= r-R; 


(I- 


-d) 3 


= 1-3*; 


I 
I — 


d 


= 1 + *; 




I 


= I+2d; 



Vi — s 



= !+£*; 



(I +<?)(I + 6)(I + £)... i + d +e + C; . 

(i_<y)(r_ e )(i_Q...i- -«-C;. 



(12) 

(13) 
(14) 
(15) 

(16) 

(17) 

(18) 

(19) 
(20) 



j) l6.] APPLICATION OF METHOD OF LEAST SQUARES. 17 

(i±tf)(i±e)(i±Q...i±<?±e±C; (21) 

%%%%% •.'•«;***CT.^ !W .... (-) 

^=^; ( 23 ) 

sin (x 4- <?) = sin x -\- 6 cos x ; (24) 

cos (# + <J) = cos* — 6 sin ^; (25) 

tan (# + d) = tan # -] 5— = tan # + S sec 8 # ; . . (26) 

COS *v 

sin (# — #) = sin ^ — (^ cos .ar ; (27) 

cos (* — d) = cos 4r + 3 sin ^ (28) 

16. The Rejection of Doubtful Observations.* — It often 
happens that in a set of observations there are certain values 
which are so much at variance with the majority that the ob- 
server rejects them in adjusting the results. This might be 
done by application of Rule 3, Article 7, provided the magni- 
tude of the errors which could not occur were definitely deter- 
mined ; but to reject such observations without proper rules is 
a dangerous practice, and not to be recommended. 

This brings into sight a class of errors which we may term 
mistakes, and which are in no sense errors of observation, such 
as we have been considering. Mistakes may result from vari- 
ous causes, as a misunderstanding of the readings, or from re- 
cording the wrong numbers, inverting the numbers, etc. ; and 
when it is certainly shown that a mistake has occurred, if it 
cannot be corrected with certainty, the observations should 
be rejected. After making allowance for all constant errors, no 
results except those which are unquestionably mistakes should be 
rejected. 

The remaining discrepancies will then fall under the head 

* See Adjustment of Observations, by T. W. Wright. N. Y., D. Van 
Nostrand. 



1 8 EXPERIMENTAL ENGINEERING. [§ 17- 

of irregular or accidental errors, and are to be corrected as ex- 
plained in the preceding articles ; the effect of a large error is 
largely or wholly compensated for by the greater frequency of 
the smaller errors. 

17. When to Neglect Errors.— Nearly all the observa- 
tions taken on any experimental work are combined with 
observations of some other quantity in order to obtain the 
desired result. Thus, for example, in the test of a steam- 
engine, observations of the number of revolutions and of the 
mean effective pressure acting on the piston are combined with 
the constants giving the length of stroke and area of piston. 
The product of these various quantities gives the work done 
per unit of time. 

All of these quantities are subject to correction, and it is 
often important to allow for such correction in the result. Just 
how important these corrections may be depends on the degree 
of accuracy which is sought. 

As the degree of accuracy increases, the number of influenc- 
ing circumstances increases as well as the difficulty of eliminat- 
ing them ; hence this part of the work is often the most difficult 
and sometimes the most important. To what limit these cor- 
rections may be carried depends on our knowledge of the laws 
which govern the experiments in question, as well as the 
accuracy with which the observations may be taken. It is 
evidently unnecessary to correct by abstruse and difficult cal- 
culation for influences which make less difference than the 
least possible unit to be determined by observation, and this 
consideration should no doubt determine whether or not correc- 
tions should be taken into account or neglected. 

Thus, in the case of the test of a steam-engine, we have 
errors made in obtaining the engine constants, i.e., length of 
stroke and area of piston. These errors may be simply of 
measurement, or they may be due to changes in the tempera- 
ture of the body measured. The errors of measurement depend 
on accuracy of the scale used, care with which the observations 
are made, and can be discussed as direct observations on a single 
quantity. The errors due to change of temperature can be cal- 



§ 18.] APPLICATION OF METHOD OF LEAST SQUARES. 1 9 

culated if observations showing the temperature are taken, and 
if the coefficient of expansion is known. A calculation will, in 
case of the steam-engine constants referred to above, show that 
in general the probable error of observation is many times in 
excess of any change due to expansion, and hence the latter 
may be neglected. The effect of errors in the other quantities 
has already been discussed in Article 11. 

It is to be remembered that the method of correction 
outlined in the " Method of Least Squares" applies only to 
those accidental and irregular errors which cannot be directly 
accounted for by any imperfection in instruments or peculiar 
habit of the observer ; usually the correction for instrumental 
and personal errors is to be made to the observations them- 
selves, before computing the probable error. 

18. Accuracy of Numerical Calculations. — The results of 
all experiments are expressed in figures which show at best 
only an approximation to the truth, and this accuracy of ex- 
pression is increased by extending the number of decimal figures. 
It is, however, evidently true that the mere statement of an ex- 
periment, with the results expressed in figures of many decimal 
places, does not of necessity indicate accurate or reliable ex- 
periments. The accuracy depends not on the number oi 
decimal places in the result, but on the least errors made in 
the observations themselves. 

It is generally well to keep to the rule that the result is to 
be brought out to one more place than the errors of observa- 
tion would indicate as accurate : that is, the last decimal place 
should make no pretensions of accuracy ; the one preceding 
should be pretty nearly accurate. In doubtful cases have one 
place too many rather than too few. No mistake, however, 
should be made in the numerical calculations ; and these, to 
insure accuracy, should be carried for one place more than is 
to be given in the result, otherwise an error may be made that 
will affect the last figure in the result. The extra place is dis- 
carded if less than 5 ; but if 5 or more it is considered as 10, and 
the extra place but one increased by 1. 

In performing numerical calculations, it will be entirely 



20 EXPERIMENTAL ENGINEERING. [§ 1 9. 

unnecessary to attempt greater 'accuracy of computation than 
can be carried out by a four-place table of logarithms, except in 
cases where the units of measurement are very small and the 
numbers correspondingly great. In general, sufficient accuracy 
can be secured by the use of the pocket slide-rule, the readings 
of which are hardly as accurate as a three-place table of loga- 
rithms. The slide-rule will be found of great convenience in 
facilitating numerical computations, and its use is earnestly 
advised. 

19. Methods of representing Experiments Graphically. 
— Nearly all experiments are undertaken for the purpose of 
ascertaining the relation that one variable condition bears to 
another, or to the result. All such experiments can be repre- 
sented graphically by using paper divided into squares. The 
result of the experiment is represented by a curve, drawn as 
follows: Lay off in a horizontal direction, using one or more 
squares as a scale, distances corresponding with the record values 
of one of the various observations, and in a similar manner, 
using any convenient scale, lay off, in a vertical direction from 
the points already fixed, distances proportional to the results 
obtained. A line connecting these various points often will be 
more or less irregular, but will represent by its direction the 
relation of the results to any one class or set of observations. 
A connecting line may form a smooth curve, but if, as is usually 
the case, the line is irregular and broken, a smooth curve should 
be drawn in a position representing the average value of the ob- 
servations. The points of observation, located on the squared 
paper as described, should be distinctly marked by a cross, or a 
point surrounded with a circle, triangle, or square; and farther, 
all observations of the same class should be denoted by the same 
mark ; so that the relation of the curve to the observations can 
be perceived at any time. 

The value of the graphical method over the numerical one 
depends largely on the well-known fact that the mind is more 
sensitive to form, as perceived by the eye, than to large num- 
bers obtained by computation. Indeed, when numbers are 



§21.] APPLICATION OF METHOD OF LEAST SQUARES. 21 

used, the averages of a series of observations are all that can 
be considered, and the effect of a gradual change, and the 
relation of that change to the result, which is often more im- 
portant than any numerical determination, is entirely disre- 
garded, and often not perceived. 

Every experiment should be expressed graphically, and stu- 
dents should become expert in interpreting the various curves 
produced. A sample of paper well suited for representing 
experiments is bound in the back portion of the present work. 

All important tests should also be accompanied by a 
graphical log; in this case time is taken as the abscissa, and the 
various observations corresponding to the time are plotted at 
convenient heights. The variation of these quantities from a 
horizontal line shows in a striking way irregularities which 
occur during the test, a horizontal line indicating uniform con- 
ditions. 

20. Area of the Diagram represents Work done.— 
In case the horizontal distances or abscissae represent space 
passed through, and the vertical distances or ordinates represent 
the force acting, then will the area included between this curve 
and the initial lines, represent the product of the mean force 
into the space passed through, — or, in other words, the work 
done. The units in which the work will be expressed will 
depend on the scales adopted. If the unit of space represent 
feet, the unit of force pounds, the results will be in foot-pounds. 
The initial lines in each case must be drawn at distances corre- 
sponding to the scales adopted, and must represent, respectively, 
zero-force and zero-space. 

21. Autographic Diagrams. — In various instruments used 
in testing, a diagram is drawn automatically, in which the ab- 
scissa corresponds to the space passed through, the ordinate 
to the force exerted, and the area to the work done. A 
familiar illustration is the steam-engine indicator-diagram, in 
which horizontal distance corresponds to the stroke of the 
piston of the engine, and vertical distance or ordinates to the 
pressure acting on the piston at any point. The absolute 
amount of the pressures may be determined by reference to the 



22 EXPERIMENTAL ENGINEERING, [§ 22. 

atmospheric line. The distance vertically between the lines 
drawn on the forward and back* strokes of the engine is the 
effective pressure acting on the piston at the given position of 
its stroke ; the mean length of all such lines is the mean 
effective pressure utilized in work. The vertical distance from 
any point on the atmospheric line to the curve drawn while the 
piston is on its forward stroke is the forward pressure, the 
corresponding distance to the back-pressure line is the back 
pressure, and the areas between these respective curves give 
effective or total work per revolution. 

An autographic device is put on many testing-machines : in 
this case the ordinates of the diagram drawn represent pres- 
sure applied to the test specimen, and abscissae represent the 
stretch of the specimen. This latter corresponds to the space 
passed through by the force, so that the area of the diagram 
included between the curve and line of no pressure represents 
the work done, — at least so far as the resistance of the test- 
piece is equal to the pull exerted, which is the case within the 
elastic limit only. 

Various dynamometers construct autographic diagrams, in 
which ordinates are proportional to the force exerted and ab- 
scissae to the space passed through, so that the area is propor- 
tional to the work done. The diagram so drawn would repre- 
sent the work done equally well were ordinates proportional 
to space passed through, and abscissae to the force exerted, but 
such diagrams are not often used. 

22. Reduction of Diagrams. — In the reduction of auto- 
graphic diagrams the process is reversed as compared with the 
construction of the diagram. The important data required are, 
first, the position of initial lines of force and of space ; second, 
the respective scales of force and of space. In computing the 
work, it is usually customary to find the mean pressure from 
the diagram, and multiply this result by the space through 
which the body actually moves, instead of multiplying by the 
length of the diagram. 

To find the length of the mean ordinate, from which the 
mean pressure is easily obtained, vertical lines are drawn so 



$ 22.] APPLICATION OF METHOD OF LEAST SQUARES. 23 

close together that the portion of the curve included between 
them is sensibly straight ; the sum of these lines, which may 
be expeditiously taken by transferring them successively to a 
strip of paper and measuring the total length, is found ; and 
this result divided by the number gives the length of the mean 
ordinate. This length multiplied by the scale gives the pres- 
sure. An integrating instrument, the planimeter, is more 
■requently used for this purpose, and gives more accurate 
results. The theory of the instrument and method of using is 
of great importance to engineers, and is given in full in the 
following chapter. 

Logarithmic Cross-section Paper is very convenient for 
the reduction of certain forms of curves to algebraic or 
analytic equations. The rulings of this paper are made at 
distances proportional to the logarithms of the numbers which 
represent the ordinates and abscissae. Any curve which may 
be represented by a simple logarithmic or exponential equa- 
tion would be represented on paper ruled in this way by a 
straight line. Thus, an equation of the general form y = 
Bx n can be reduced so that log y = log B -\- n log x, which 
is the equation of a straight line in logarithmic units. In 
this equation n is the tangent of the angle which the line 
makes with the axis of abscissae, and B is the intercept on this 
axis from the origin. Paper ruled in this manner can be ob- 
tained from most dealers in technical supplies. In case it 
cannot be obtained, ordinary cross-section paper, as shown in 
the Appendix to this book, may be used by numbering the 
graduations on the axes of abscissae and ordinates as propor- 
tional to the logarithms of the distances from the origin. 



CHAPTER II. 

APPARATUS FOR REDUCTION OF EXPERIMENTAL DATA 
AND FOR ACCURATE MEASUREMENT. 

23.The Slide-rule. — The slide-rule is made in several forms, 
but it consists in every case of a sliding scale, in which the 
distance between the divisions, instead of corresponding to the 
numbers marked en the scale, corresponds to the logarithms of 
these numbers. This scale can be made to slide past another 
logarithmic scale, so that by placing them in proper positions 
there may be shown the sum or difference of these scales, and 
the number corresponding. As these scales are logarithmic, the 
number corresponding to the sum is the product, that corre- 
sponding to the difference is the quotient. Operations involv- 
ing involution and evolution can also be performed. Scales 
showing the logarithmic functions of angles are also usually 
supplied. 




m... V ii V ., V iiy„ v VIV"V"y"^ , T" , T"S"n'"V'"V"^ 




[iii|tiiiili|iit i t i ] iT.M 1 













Fig. i. — The Slide-rule. 



The usual form of the slide-rule is shown in Fig. I. This 
form carries four logarithmic scales, one on either edge of the 
slide, and one above and one below. Either scale can be used; 
that above is generally to one half the scale of the lower, and 
while not quite as accurate, is more convenient than the one 
below. The trigonometrical scales are on the back of the slide. 

24 



§24.] APPARATUS. 2$ 

The principal use to the computer is the solution of problems 
in multiplication and division. 

The following directions for use of the plain slide-rule, 
which is ordinarily employed, give a simple practical method 
of multiplying or dividing by the slide-rule, experience 
having shown that when these processes are fully understood 
the others are mastered without instruction. 

Suppose that a student has a slide-rule of the straight kind, 
and similar to the one in Fig. I, which consists of a stationary 
scale, a sliding-scale, and a sliding pointer or runner. These 
parts we will term, respectively, the " scale," the slide, and the 
runner. 

24. Directions for using the Slide-rule. — Holding the 
rule so that the figures are r'ght side up, four graduated edges 
will be seen, of which only the upper two are used in the 
problem we are about to describe. (The method of using the 
two lower scales would be exactly the same, the difference 
being, that they are twice as long, and that the slide is above 
instead of below the scale.) 

Move the slide to such a position that the graduations 
agree throughout the length of the scale, and place the runner 
at a division marked 1, and the rule is ready for use. Arrange 
the factors to be dealt with in the form of a fraction, with one 
more factor in numerator than in denominator, units being in- 
troduced if necessary to make up deficiencies in the factors. 

Thus, to multiply 6 by 7 by 3 and divide by 8 times 2, 
arrange the factors as follows : 

6X7X3 
8X2* 

The factors in the numerator show the successive positions 
which the runner must take ; those in the denominator the 
positions of the slide. Thus, to solve above example, start (1) 
with runner at 6 on the scale, always reading from same side of 
runner; (2) bring figure 8 on slide to runner; (3) move runner 
to 7 on slide : the result can now be read on the scale ; (4) 



26 EXPERIMENTAL ENGINEERING. [§ 24. 

bring 2 on slide to runner ; (5) move runner to 3 on slide. The 
result is read directly on the scale at position of runner. 

Another example : Multiply 11 by 6 by 7 by 8, and divide 

by 31. 

In this case arrange the factors 

11 X 6 X 7 X 8 
1 X 1 X 31 

Start with runner at 11 on scale, move 1 on slide to runner, 
move runner to 6 on slide, move 1 on slide to runner, runner 
to 7 on slide, move 31 on slide to runner, runner to 8 on slide: 
read result on scale at runner. 

The numbers on the slide-rule are to be considered signifi- 
cant figures, and to be used without regard to the decimal 
point. Thus the number on the rule for 8 is to be used as .8 
or 80 or 800, as may be desired, even in the same problem. 
The significant figures in the result are readily determined by 
a rough computation. In case the slide projects so much 
beyond the scale, that the runner cannot be set at the required 
figure on the slide, bring the runner to 1 on the slide, then 
move the slide its full length, until the other 1 comes under 
the runner. Then proceed according to directions above ; i.e., 
move runner to number on slide, and read results on the scale : 



6 X 25 X 3-5 X 7 X 7 X 3i _ ? 
n X 426 X 914 X 1 X 1 



Begin with the first factor in the numerator, and multiply 
and divide alternately, — 

X 6, ^ 7T, X 25, -j- 426, X 3-5> -5- 9 X 4> etc.,— 

until all the factors have been used, checking them off as they 
are used, to guard against skipping any or using one twice. 



§24.] APPARATUS. 2J 

To multiply, move the runner; to divide, move the slide: in 
either case see that the runner points to a graduation on the 
slide corresponding to the factor. The result at the end or at 
any stage of the process is given by the runner on the station- 
ary scale. Or, to be more exact, the significant figures of the 
result are given, for in no case does the slide-rule show where 
to place the decimal point. If the decimal point cannot be 
located by inspection of the factors, make a rough cancel- 
lation. 

Involution and evolution are readily mastered by 
simple practice. Slide-rules working on the same prin- 
ciple are frequently made with circular or cylindrical scales, 
which in the Thacher and Fuller instruments are of great 
length. 

Thacher's calculating instrument consists of a cylinder 4 
inches in diameter and 18 inches long, working within a frame- 
work of triangular bars. Both the cylinders and bars are grad- 




Fig. 2. — Thacher's Calculating Instrument. 

uated with a double set of logarithmic scales, and results in 
multiplication or division can be obtained from one setting of 
the instrument, hence it is especially convenient when a series 
of numbers are to be multiplied by a common factor. The 
scales in this instrument are about 50 feet in length, and results 
can be read usually to five places. 

The instrument is similar to the straight slide-rule previously 
described, the scale on the triangular bars corresponding to the 
stationary scale, that on the cylinder to the sliding scale, and a 
triangular index / to the sliding pointer or runner. The method 
of using is essentially similar to that of the plain slide-rule ; 



28 



EXPERIMENTAL ENGINEERING. 



[§24- 



thus, to solve an example of the form a/b, put the runner / on 
the triangular scale at the number corresponding to a, bring 
the number corresponding to b on the cylindrical scale to 
register with a on the triangular scale ; the respective numbers 
on the trianglar scale and cylinder will in this position all be in 
the ratio of a to b, and the quotient will be read by noting that 
number on the triangular scale which registers with I on the 
cylindrical scale. The product of this quotient by any other 
number will be obtained by reading the number on the trian- 
gular scale registering with the required multiplier on the cylin- 
drical scale. 

Fuller's slide-rule consists of a cylinder C which can be 
moved up or down and turned around a sleeve which is attached 
to the handle H. A single logarithmic scale, 42 feet in length, 




Fig. 



-The Fuller Slide-rule. 



is graduated around the cylinder spirally, and the readings are 
obtained by means of two pointers or indices, one of which, A, 
is attached to the handle, and the other, B, to an axis which 
slides in the sleeve. This instrument is not well adapted for 
multiplying or dividing a series of numbers by a constant, since 
the cylinder must be moved for every result. The instrument 
is, however, very convenient for ordinary mathematical com- 
putations, and the results may be read accurately to four deci- 
mal places. 

The method of using the instrument is as follows : Call the 
pointer^, fixed to the handle, the fixed pointer, the other BB\ 
which may be moved independently as the movable index. 
To use the instrument, as for example in performing the oper- 
ation indicated by {a X b) ~- c, set the fixed pointer A to the 
first number in the numerator, then bring the movable index 



§ 25-] APPARATUS. 29 

B to the first figure in the denominator; then move the cy- 
linder C until the second figure in the numerator appears under 
the movable index, finally read the answer on the cylinder C 
underneath the fixed pointer A. 

In general, to divide with this instrument move the index 
B; to multiply, move the cylinder C\ read results under the 
fixed pointer A. The movable index BB' has two marks, 
one at the middle, the other near the end of the pointer, either 
of which may be used for reading, as convenient, their distance 
apart corresponding to the entire length of the scale on the 
cylinder C. 

25. The Vernier. — The vernier is used to obtain finer sub- 
divisions than is possible by directly dividing the main scale, 
which in this discussion we will term the limb. 

The vernier is a scale which may be moved with reference 
to the main scale or limb, or, vice versa, the vernier is fixed 
and the limb made to move past it. 

The vernier has usually one more subdivision for the same 
distance than the limb, but it may have one less. The 
theory of the vernier is readily perceived by the following 
discussion. Let d equal the value of the least subdivision 
of the limb; let 11 equal the number of subdivisions of 
the vernier which are equal to n — 1 on the limb. Then the 

value of one subdivision on the vernier is d[ 

\ 71 

The difference in length of one subdivision on the limb and 
one on the vernier is 

j-j[ n 



11 1 n 

which evidently will equal the least reading of the vernier, and 
indicates the distance to be moved to bring the first line of 
the vernier to coincide with one on the limb. In case there is 
one more subdivision on the limb than on the vernier for the 
same distance, the interval between the graduations on the 
vernier is greater than on the limb, and the vernier must be 



30 EXPERIMENTAL ENGINEERING. [§ 2& 

behind its zero-point with reference to its motion, and hence is 
termed retrograde. The formula for this case, using the same 

notation as before, gives d\ ) —d=— for the least reading. 

The following method will enable one to readily read any 
vernier: i. Find the value of the least subdivision of the limb. 
2. Find the number of divisions of the vernier which corre- 
sponds to a number one less or one greater than that on the 
limb: the quotient obtained by dividing the least subdivision 
of the limb by this number is the value of the least reading of 
the vernier. The following rules for reading should be care- 
fully observed : 

Firstly. Read the last subdivision of the limb passed over by 
the zero of the vernier on the scale of the limb as the reading of 
the limb. 

Secondly. Look along the vernier until a line is found which 
coincides with some line on the limb. Read the number of this 
line from the scale of the vernier. This number multiplied by 
the least reading of the vernier is the reading of the vernier. 

Thirdly. The sum of these readings is the one sought. 

Thus, in Fig. 5, page 31, (1) the reading of the limb rs 4.70 
at a\ (2) that of the vernier is 0.03 ; (3) the sum is 4.73. 

26. The Polar Planimeter. — The planimeter is an instru- 
ment for evaluating the areas of irregular figures, and in some 
one of its numerous forms is extensively used for finding the 
areas of indicator and dynamometer diagrams. 

The principal instrument now in use for this purpose was 
invented by Amsler and exhibited at the Paris Exposition in 
1867. This form is now generally known as Amsler's Polar 
Planimeter; as most of the other instruments are modifications 
of this one, it is important that it be thoroughly understood. 

The general appearance of the instrument is shown in Fig. 
4, from which it is seen that it consists of two simple arms PK 
and FK t pivoted together at the point K. The arm /^during 
use is free to rotate around the point P, and is held in place by 
a weight. The arm KF carries at one end a tracing-point, 
which is passed around the borders of the area to be integrated 



26.] 



APPARA TUS. 



31 



It also carries a wheel, whose axis is in the same vertical plane 
with the arm KF, and which may be located indifferently be- 
tween AT and F, or in KF produced. It is usually located in KF, 
produced as at D. The rim of this wheel is in contact with 
the paper, and any motion of the arm, except in the direction 
of its axis, will cause it to revolve. A graduated scale with a 
vernier denotes the amount of lineal travel of its circumference. 
This wheel is termed the record-wheel. 




Fig. 4. — Amsler's Polar Planimeter. 



The detailed construction of the record-wheel, and the ar- 
rangement of the counter G, showing the number of revolutions, 




Fig. 5.— The Record-wheel. Amsler's Polar Planimeter. 



is shown in Fig. 5. The wheel D is subdivided into a given 
number of parts, usually 100 ; the value of one of these parts is 
to be obtained by dividing the circumference of the rim of the 
wheel which is in contact with the paper by the number of. 



3 2 EXPERIMENTAL ENGINEERING. [§ 27 . 

divisions. This result will give the value of the least division on 
the limb; this is subdivided by an attached vernier, in this par- 
ticular case to tenths of the reading of the limb, so that the least 
reading of the vernier is one thousandth of that of one revolution. 

27. Theory of the Instrument. (See Fig. 9.) — The Zero- 
circle. — If the two arms be clamped so that the plane of the record- 
wheel intersects the centre P, and be revolved around P, the 
graduated circle will be continually travelling in the direction of 
its axis, and will evidently not revolve. A circle generated under 
such a condition around P as a centre is termed the zero- circle. 
If the instrument be undamped and the tracing-point be moved 
around an area in the direction of the hands of a watch outside 
the zero-circle, the registering wheel will give a positive record • 
while if it be moved in the same direction around an area inside 
the zero-circle, it will give a negative record. This fact makes it 
necessary, in evaluating areas that are very large and have to be 
measured by swinging the instrument completely around P as a 
centre, to know the area of this zero-circle, which must be added 
to the determination given by the instrument, since for such cases 
that circumference is the initial point for measurement. 

Geometrical and Analytical Demonstration. — If a straight line 
mn move in a plane, it will generate an area. This area may be 
considered positive or negative according to the direction of 
motion of the line. In Fig. 6, let the paths of the ends m and n 
of the line be the perimeters of the areas A and B respectively; 
then it is at once apparent that the net area generated is A + C — 
C—B or A— B. The immediate corollary to this is that if the 
area B be reduced in width to zero, i.e., become aline along which 
n travels back and forth, the area swept over will be A, around 
which m is carried. 

Analyzing a differential motion of the line from mn to m'n' 
(Fig. 8), it may be broken up into three parts: a movement per- 
pendicular to the line, giving area Idp; a movement in the direc- 
tion of the length of the line, giving no area; and a movement 
of rotation about one end, giving as area \PdQ. The total differ- 
ential of area is then dA=ldp + %l 2 dd. I is always a constant 






§27-] 



APPARATUS. 



33 



during the operation of a planimeter, so that A= j dA=lj dp + 

wfdd. 

The common use of a planimeter is that typified in Fig. 7, 
where the tracing-point is carried around the area to be meas- 
ured, while the other end of the tracing-arm is guided back and 
forth along some line. The guide-line is usually either a straight 
line or an arc of a circle. When the tracing-point has returned 
to its initial position the net angle turned through by the tracing- 
arm, or j ddj is zero. Hence A =lj dp x simply. But j dp is 

the net distance the arm has moved perpendicular to itself. 
Call this R, and there results the equation of the planimeter 
A=l-R. 





Fig. 6. 



Fig. 7. 



If the polar planimeter is so used as to bring in the zero-circle, 
the case is that of Fig. 6, each end of the line describing an area. 
The tracing-arm sweeps over the difference between the area 
described by T (Fig. 9) and the circle made by G about P as 
centre. This difference-area is not, however, recorded by the 

planimeter because the / dd is now 2tz instead of zero, T making 

a complete revolution about G. The linear turning of the edge 

of the recording- wheel is I dp — 27m, where n is the distance from 

guided point G to the plane of the wheel. The effect on the 
reading is the same as if the radius PG were increased. The 



34 EXPERIMENTAL ENGINEERING. [§ 2J 

zero- circle is traced by T when the plane of W passes through 

P. Then jdp = 27tn, and the wheel records zero. 

In practice the area described by the tracing-point is found 
by adding to the area of the zero- circle the area recorded by the 
wheel, taking account of the algebraic sign of the latter. 





Fig. 8. 



Fig. 9. 



The following demonstration is of German origin and, 
although less general in its nature, is retained for the reason 
that it is more satisfactory to some minds than the one given 
above. 

Movement of the Record-wheel. (Fig. 10.) — From the preced- 
ing discussion it is seen that the record- wheel does not register, 
so long as its plane is radial, or so long as angle ED'F" = 90 . 
The amount of rotation due to variation in the angle EJD 
between the arms is, if an area be completely circum- 
scribed, equal in opposite directions, and hence does not 
affect the result, so that it is necessary to discuss merely the 
case of motion around the pole E, with the angle EJD fixed. 
Thus, for instance, suppose angle EJD to remain constant, and 
the tracing-point to swing through the infinitesimal angle F"EF, 
designated by dd, the record-wheel would move near the path 
DD' more or less irregularly, but subtending an equal angle 
DED' '. The component of this motion which constitutes the 
record is OD f , designated by dR, which is the projection of 



§27.] APPARATUS. 35 

this path on a perpendicular to JF. Since DED' is infinitesi- 
mal, and dd = tan dd, we have 



DD' = Z>£tftf ; also dR = OD' = DD' cos ED'D ; 

but ED'D = isZ>c9 from similar triangles. Hence 

dR = ED cos EDOdd. 

Denote the length of arm EJ by m, the length of arm JF from 
pivot to tracing-point by /, the distance /X> from pivot to record- 
wheel by n, the angle EJD by B. Let fall a perpendicular 
from E on FD, or FD produced at 0. Then we have 

EDcosEDO = <9Z> =JO-JD = mcosB — n. 

Hence 

dR = (m cos B — n)dd (i) 

Second, the infinitesimal area FtF"t' , lying adjacent to the 
zero-circle. — Let EF = r, let ZjF" = r', the radius of the 
zero-circle. Let dA = the area sought. Let dd = FEt. 
Then 

area /?£/ = £rW0, 

and 

area F"£/' = \r n dd. 

Then 

dA^FEt-F f, Et f = ^-^)de. . . . (2> 

From the oblique triangle Zj/F, 

r* = »2 3 + /* + 2mlcosB • (3) 



36 EXPERIMENTAL ENGINEERING. [§ 27. 

From the right triangle ED ' F n ', 

r ri zzztn' + S -\-2nl. ....'.... (4) 
Substituting the values of r % and r' 2 in equation (2), we have 

dA = /(mcosB — n)dd. ...... (5) 

By comparing equation (5), the differential equation for the 
area, with equation (1), the corresponding equation for the 




Fig. 10. — Polar Planimeter. 



record, we see that 



dA = ldR\ , . . . . . . (6) 

or by integration between limits o and R, since / is a constant, 

A=IR (7) 

This shows that the area is equal, to the length of arm 
from pivot to the tracing-point, multipliea by the space registered 



§ 28.] APPARA TUS. 37 

on the circumference of the record-wheel, and is independent of 
the other dimensions of the instrument. 

That this is true for areas not adjacent to the zero-circle, 
or for areas partly inside and out, can readily be proved by 
subtracting the areas between the zero-circle and the given 
area, or by a similar process. Hence the demonstration is 
general. 

The Amsler instrument is usually constructed so that the 
arm / is adjustable in length, and consequently it may be 
made available for any scale or for various units. Gradua- 
tions are engraved on the arm which show the length required 
to give a record in a given scale or for given units. 

The area of tJie zero-circle is usually engraved on the top 
of the arm /. In case it is not given, it may be found by 
evaluating the areas of two circles of known area, each greater 
than the area of the zero-circle nr'*. Let the areas of such 
circles be respectively C and C' t and the corresponding read- 
ings of the record-wheel R and R\ in proper units. Then we 
have 

C = nr' 2 + R and C = nr n + R\ 
from which 

27tr'* = C-\-C -(R+R f ) (8) 

Having found r' 2 , we can compute n, since r'* = m* + / 2 + 2nl t 
and m and / can both be obtained from measurement. 

28. Forms of Polar Planimeters. — Polar planimeters are 
made in two forms: I. With the pivot/, Fig. io, fixed. 2. With 
pivot J movable, so that the arm / between pivot and tracing- 
point may be varied in length. Since the area is in each case 
equal to the length of this arm, multiplied by the lineal space 
R moved through by the record-wheel, we have in the first 
case, since / is not adjustable, the result always in the same 
unit, as square inches or square centimeters. In this case it is 



38 EXPERIMENTAL ENGINEERING. [§ 2& 

customary to fix the circumference of the record-wheel and 
compute the arm / so as to give the desired units. 

For example, the circumference of the record-wheel is. 
assumed as equal to 100 divisions, each one-fortieth of an inch, 
thus giving us a distance of 2.5 inches traversed in one revolu- 
tion. The diameter corresponding to this circumference is 
0.796 inch, which is equal to 2.025 centimeters. The distance 
from pivot to tracing-point can be taken any convenient dis- 
tance : thus, if the diameter of the record-wheel is as above, 
and the length of the arm be taken as 4 inches, the area 
described by a single revolution of the register-wheel will be 
2.5 X 4 = 10.0 square inches. 

Since there were 100 divisions in the wheel, the value of 
one of these would be in this case 0.1 square inch. This would 
be subdivided by the attached vernier into ten parts, giving as 
the least reading one one-hundredth of a square inch. By mak- 
ing the arm larger and the wheel smaller, readings giving the 
same units could be obtained. 

The formula expressing this reduction is as: follows : Let d 
equal the value of one division on the record-wheel ; let / equal 
the length of the arm from pivot to tracing-point ; let A equal 
the area, which must evidently be either 1, 10, or 100 in order 
that the value of the readings in lineal measures on the record- 
wheel shall correspond with the results in square measures. 
Then by equation (7) we shall have, supposing 100 divisions, 



IOO dl— A; (8) 



/= i^ fe> 



If A = iO square inches and d = ^ inch, 



2-5 



§ 29.I APPARA TUS. ' 39 

If A = 10 square inches and d = -fo inch, 



/-=-* 



The length of the arm from centre to the pivot has no effect 
on the result unless the instrument makes a complete revolu- 
tion around the fixed point E, in which case the area of the 
zero-circle must be considered. It is evident, however, that 
this arm must be taken sufficiently long to permit free motion 
of the tracing-point around the area to be evaluated. 

The second class of instruments, shown in Fig. 2, are 
arranged so that the pivot can be moved to any desired posi- 
tion on the tracing-arm KF, or, in other words, the length can 
be changed to give readings in various units. The effect of 
such a change will be readily understood from the preceding 
discussion. 

29. The Mean Ordinate by the Polar Planimeter.— 
If we let/ equal the length of the mean ordinate, and let L 
equal the length of the diagram, then the area A = Lp, but 
the area A = IR [eq, (7)]. Therefore Lp — IR, from which 

l+L=p-±R (10) 

In an instrument in which / is adjustable, it may be made 
the length of the area to be evaluated. Now if / be made 
equal L, p = R. That is, if the adjustable arm be made equal 
to the length of the diagram^ the mean ordinate is equal to the 
reading of the record-wheel, to a scale to be determined. 

The method of making the adjustable arm the length of 
the diagram is facilitated by placing a point U on the back of 
the planimeter at a convenient distance back of the tracing- 
point F and mounting a similar point Fat the same distance 
back of the pivot C\ then in all cases the distance UVyriM be 
equal to the length of the adjustable arm /. The instrument is 
readily set by loosening the set-screw 5 and sliding the frame 



4Q 



EXPERIMENTAL ENGINEERING. 



L§ 29. 



carrying the pivot and record-wheel until the points c^Fare at 
the respective ends of the diagram to be traced, as shown in 
Fig. 11. 

In the absence of the points U and V the length of the 
diagram can be obtained by a pair of dividers, and the distance 
of the pivot C from the tracing-point F made equal to ihe 
length of the diagram. 

In this position, if the tracing-point be carried around the 
diagram, the reading will be the mean ordinate of the diagram 




Fig. 



-Method of Setting the Planimeter for Finding the Mean Ordinate. 



expressed in the same units as the subdivisions of the record- 
wheel ; thus if the subdivisions of this wheel are fortieths of 
one inch, the result will be the length of the mean ordinate in 
fortieths. This distance, which we term the scale of the record- 
wheel, is not the distance between the marks on the graduated 
scale, but is the corresponding distance on the edge of the 
wheel which comes 'in contact with the paper. 

The scale of the record-wheel evidently corresponds to a 
linear distance, and it should be obtained by measurement or 
computation. It is evidently equal to the number of divisions 
in the circumference divided by nd, in which d is the diameter, 
or it can be obtained by measuring a rectangular diagram with 
a length equal to /, and a mean ordinate equal to one inch, in 
which case the reading of the record-wheel will give the num- 
ber of divisions per inch. A diameter of 0.795 inch, which 
corresponds to a radius of one centimeter, with a hundred sub- 



32-] 



APPARA TUS. 



41 



divisions of the circumference, corresponds almost exactly to 
a scale of forty subdivisions to the inch, and is the dimension 
usually adopted on foreign-made instruments. 

30. The Suspended Planimeter. — In the Amsler sus- 
pended planimeter as shown in Fig. 12, pure rolling motion 
without slipping is assumed to take place. The motion of the 
record-wheel, not clearly shown in the figure, is produced by 
the rotation of the cylinder c in contact with the spherical 




Suspended Planimeter. 



segment R. The rotation of the segment is due to angular 
motion around the pole O, that of the cylinder c to its posi- 
tion with reference to the axis of the segment. This position 
depends on the angle that the tracing arm, ks f makes with the 
radial arm, BB. The area in each case being, as with the 
polar planimeter, equal to the product of the length of tracing 
arm from pivot to tracing point multiplied by a constant 
factor. 

31. The Coffin Planimeter and Averaging Instrument. 
— This instrument is shown in Fig. 13, from which it is seen 
that it consists of an arm supporting a record-wheel whose axis 
is parallel to the line joining the extremities of the arm. This 
instrument was invented by the late John Coffin, of Johnstown, 
in 1874. The record-wheel travels over a special surface ; one 
end of the arm travels in a slide, the other end passes around 
the diagram. 

32. Theory of the Coffin Instrument. — This planimeter 
may be considered a special form of the Amsler, in which the 
point P, see Fig. 14, page 43, moves in a right line instead of 



42 



EXPERIMENTAL ENGINEERING. 



[§32- 



swinging in an arc of a circle, and the angle CPT, correspond- 
ing to B in eq. (1), is a fixed right angle. The differential 
equation for area therefore is 

dA=lndd, (il) 




Fig. 13.— The Coffin Averaging Instrument. 

and the differential equation of the register becomes 

dR — ndd s2) 

Hence, as in equation (7), 

A = IR (13) 



§32-] 



APPARA TUS. 



43 



That is, the area is equal to the space registered by the record- 
wheel multiplied by the length of the planimeter arm. 

This instrument may be made to give a line equivalent to 
the mean ordinate (M. ) by placing the diagram so that 




Fig. 14. — Coffin Averaging Instrument. 



one edge is in line with the guide for the arm ; starting at the 
farthest portion of the diagram, run the tracing-point around 
in the usual manner to the point of starting, after which run 
the tracing-point perpendicular to the base along a special 
guide provided for that purpose until the record-wheel reads 
as at the beginning. This latter distance is the mean 
ordinate. 



44 EXPERIMENTAL ENGINEERING. [§ 33* 

To prove, take as in Art. 29 the M. O. = /, the length 
of diagram = Z, the perpendicular distance = S. Then 

A = pL=/R. ......... (14) 

Let C be the angle, EPT, that the arm makes with the guide, 
Fig. 8. In moving over a vertical line this angle will remain 
constant, and the record will be 

R = 5 sin C. . • . . . . . o (15) 
For the position at the end of the diagram 

sin C '= L -f- /; 

therefore 

R=SL+L 

Substituting this in equation (14), 

pL = IR = ISL + 1 = SL. 

Hence p = 5 (15^), which was to be proved. . 

From the above discussion it is evident that areas will be 
measured accurately in all positions, but that to get the 
M. O. the base of the diagram must be placed perpendicular 
to the guide, and with one end in line of the guide pro- 
duced. 

It is also to be noticed that the record-wheel may be placed 
in any position with reference to the arm, but that it must have 
its axis parallel to it, and that it registers only the perpen- 
dicular distance moved by the arm. 

33. The Willis Planim eter. — This planimeter is of the 
same general type as the Amsler Polar, but in place of the record - 
wheel for recording-arm it employs a disk or sharp-edged wheel 
free to slide on an axis perpendicular to the tracing-arm. The 
distance moved perpendicular to this arm is read on the graduated 



§ 34-] APPARATUS. 4$ 

edge of a triangular scale which is supported in an ingenious man- 
ner, as shown in the accompanying figure. The planimeter-anri 
can be adjusted as in the Amsler Planimeter so as to read the 
M. E. P. direct. An adjustable pin, E, is employed for the 
purpose of setting off the length of the diagram. 

The mathematical demonstration is exactly as for the Amsler 
Planimeter, but in this case it is evident that the perpendicular 
distance which is registered on the scale is independent of the 




Fig. 14a. — The Willis Planimeter. 

circumference of the wheel. The only conditions of accuracy- 
are, that the axis of the scale shall be at right angles to the 
arm of the planimeter, and that its graduations shall be 
equal to the area to be measured divided by the length of trie- 
arm. 

34. The Roller-planimeter. — This is the most accurate^ of 
the instruments for integrating plane areas, and is capable of 
measuring the area of a surface of indefinite length and of lim- 
ited breadth. This instrument was designed by Herr Corradi of 
Zurich, and is manufactured in this country by Fauth & Com- 
pany of Washington, D. C. 

A view of the instrument is shown in Fig. 15. The features 
of this instrument are: firstly, the unit of the vernier is so 
small that surfaces of quite diminutive size may be determined 
with accuracy; secondly, the space that can be encompassed 
bv one fixing of the instrument is very large; thirdly- the 



4 6 



EXPERIMENTAL ENGINEERING. 



[§34- 



results need not be affected by the surface of the paper on 
which the diagram is drawn ; and, fourthly, the arrangement of 
its working parts admit of being kept in good order a long 
time. 

The frame B is supported by the shaft of the two rollers 
R X R X , the surfaces of which are fluted. To the frame B are 
fitted the disk A, and the axis of the tracing-arm F. The whole 
apparatus is moved in a straight line to any desired length 
upon the two rollers resting on the paper, while the tracing- 
point travels around the diagram to be integrated. Upon the 
shaft that forms the axis of the two rollers R X R X a minutely 




FlG. 15. — R.OLLER-PLANIMETER* 

divided mitre-wheel R, is fixed, which gears into a pinion 
R 2 . This pinion, being fixed upon the same spindle as the 
disk^4, causes the disk to revolve, and thereby induces the roll- 
ing motion of the entire apparatus. 

The measuring-roller E, resting upon the disk A, travels 
thereon to and fro, in sympathy with the motion of the tracing- 
arm F, this measuring-roller being actuated by another arm 
fixed at right angles to the tracing-arm and moving freely 
between pivots. The axis of the measuring-roller is parallel to 
the tracing-arm F. The top end of the spindle upon which 






§35-] APPARATUS. 47 

the disk A is fixed pivots on a radial steel bar CC X , fixed upon 
the frame B. 

35. Theory. — The following theory of the roller-plan im- 
eter is partly translated from an article by F. H. Reitz, in the 
Zeitschrift fur Vermessungs-Wesen, 1884. 

According to the general theory of planimeters furnished 
with measuring-rollers, it is immaterial what line the free end 
of the tracing-arm travels over ; nevertheless there is some 
practical advantage in the construction of the apparatus to be 
obtained from causing that end to travel as nearly as possible 
in a straight line. Still it is obvious that a slight deviation 
from the straight line would not involve any inaccuracy in the 
result. 

Seeing that the fulcrum of the tracing-arm keeps travelling 
in a straight line, it appears advisable, in evolving the theory 
of the apparatus, to assume a rectangular system of co-ordinates, 
and fix upon the line along which that fulcrum travels as the 
axis of abscissae. 

The passage of the tracing-point around the perimeter of a 
diagram maybe looked upon as being made up of two motions 
— one parallel to the axis of abscissae and the other at right 
angles to that axis. Inasmuch as the latter of these two 
motions, in the direction of the axis of ordinates, is after all 
but an alternate motion of the tracing-point which takes place 
in an equal ratio until the tracing-point has returned to its 
starting-point, no one point of the circumference of the measur- 
ing-roller is continuously moved forward in consequence of this 
motion. Therefore it is only necessary to take the differential 
motion of the tracing-point in the direction of the axis of 
abscissae into consideration. 

In Fig. 16 the same letters of reference denote identical parts 
or organs as in Fig. 15 and the position of the parts in the two 
figures correspond exactly, the letter D denoting the distance 
between the fulcrum of the tracing-arm and the axis of the 
disk A. The amount of motion of a point on the record- 
wheel E, while the tracing-point travels to the extent of dx> 
must be determined. If the construction of the planimeter is 



48 



EXPERIMENTAL ENGINEERING. 



[§35- 



correct, this quantity must be the product of a constant derived 
from the instrument, multiplied by the differential expression 
for the surface. This latter quantity with reference to rectan- 
gular co-ordinates is ydx. 

It is readily seen that as the tracing-point moves an amount 
equal to dx, a point in the circumference of the rollers R X R X 
must be shifted the same amount, since the axes of these rollers 
are parallel to the ordinate y. 

Any point in the pitch-line of the mitre-wheel R % must move 

an amount equal to ~^dx. 




Fig. 16. 



Suppose that while the tracing-point moves a distance dx % 
the disk A moves a distance ab, Fig. 10, since this disk is turned 
foy the mitre-wheel whose pitch-circle is R % , and ad is the dis- 
tance from record-wheel to the axis of this wheel, we must 
have 



R a ad 



(16) 



§35-] 



APPARA TUS. 



49 



Because of the position of the axis of the record-wheel E> the 
motion of the disk A to the extent of ab produces a shifting 
of a point in the circumference of E equal to cb, while the 
record-wheel slips a distance ac. The distance cb is the reading 
of the record-wheel and is the quantity required. We have 
dab = 90 , cag — 90 ; hence caf = a y and fab = fi, and cab 
= «-)-/?. So that since acb — 90 , 

cb = ab sin (a -f- /3) = ab (sin a cos fi -J- cos a sin /?). , (17) 

But it is seen that 



sin a = jf. 



Hence 



cos a = 



= \A - w' 



. „ af sin t* <z£v 



^ 



^ 



/fc</' 



" ad ad 

Substitute these values in equation (17): 

~7 



cb=ab- 




yD 



(18) 



Substitute the value of ab in (16), 

cb = jfxy^* — (constant) ydx % . • • • (19) 
which was to be proved. 



50 EXPERIMENTAL ENGINEERING. [§ 36. 

The differential distance cb is the reading of the record* wheel , 
let this be represented by dr t denote by C the constant - fr D ' ; 
then 

dr = Cydx; ydx =-£', I ydx^L J j r% 

This expression integrated gives 

Area = ^(r 1 -^) = --^-(r 1 -r t ); . . <2C) 

in which r, and r 9 are the initial and final readings of the 
record-wheel. 

In the construction of the instrument R l9 R 39 D 9 and R 2 are 
fixed quantities, but the length of the tracing-arm F can be 
varied, with a corresponding variation in the unit of measure- 
ment. 

36. Care and Adjustment of Planimeters. — From the 
preceding discussion it is seen that the area in every case is 
the product of the distance actually moved by the circum- 
ference of the record-wheel into the length of the arm from 
the tracing-point to the pivot, into a constant which may be 
and is, in the polar planimeter, equal to one. It is also to be 
noticed that the record-wheel is so arranged as to register the 
distance moved by a point in a direction perpendicular to that 
of the tracing-arm, and that for other directions it slips. This 
indicates that any change whatever in the diameter of the 
record-wheel or gear-wheels, due to wear or dirt, will require a 
corresponding change in the length of tracing-arm ; and further, 
any irregularities in the edge of this wheel will make the rela- 
tive amounts of slipping and rolling motion uncertain, and con- 
sequently impair its accuracy. 

Again, the plane of the record-wheel must be perpendicular 
to the tracing-arm, otherwise an error will result. 

In the planimeter the moving parts usually Lave pivot- 



§37-] APPARATUS. 51 

bearings which can be loosened or tightened as required. The 
revolving parts should spin around easily but at the same time 
accurately, and the various arms should swing easily and show 
no lost motion. The pitch-line of the record-wheel should be 
as close as possible to the vernier, but yet must not touch it; 
the counting-wheel must work smoothly, but in no way inter- 
fere with the motion of the record-wheel. 

37. Directions for Use. — 1. Oil occasionally with a few 
drops of watch or nut oil. 

2. Keep the rim of the record-wheel clean and free from 
rust. Wipe with a soft rag if it is touched with the ringers. 

3. Prepare a smooth level surface, and cover it with heavy 
drawing-paper, for the record-wheel to move over. Stretch 
the diagram to be evaluated smooth. 

4. Handle the instrument with the greatest care, as the 
least injury may ruin it. Select a pole-point so that the instru- 
ment will in its initial position have the tracing-arm perpen- 
dicular either to the pole-arm or to the axis of the fluted 
rollers, as the case may be ; for in this position only is the 
error neutralized, which arises from the fact that the tracer is 
not returned to its exact starting-point. Then marking some 
starting-point, trace the outline of the area to be measured in 
the direction of the hands of a watch, slowly and carefully, 
noting the reading of the record-wheel at the instant of start- 
ing and stopping. It is generally more accurate to note the 
initial reading of the record-wheel than to try and set it at zero. 

5. Special Directions. — To obtain the mean ordinate with 
the polar planimeter, make the length of the adjustable arm 
equal to the length of the diagram, as explained in Art. 28, 
page 38, and follow directions for use as before. 

6. In using the Coffin planimeter, the grooved metal plate / 
is first attached to the board, upon which the apparatus is 
mounted as shown in the cut, page 42, being held in place by 
a thumb-screw applied to the back side. 

The diagram will be held securely in place by the spring-clips 
adjacent, A and C, Fig. 13. The area may be found by running 
the tracing-point around the diagram, as described for the 



52 EXPERIMENTAL ENGINEERING. [§ 38. 

polar planimeter, for any position within the limits of the arm. 
The mean ordinate may be found by locating the diagram as 
shown in the cut, with one extreme point in the line of the 
metal groove produced, and the dimension representing the 
length of the diagram perpendicular to this groove. Start to 
trace the area at the farthest distance of the diagram from the 
metal guide produced, as shown in Fig. 13 ; pass around in the 
direction of the motion of the hands of a watch to the point 
of beginning ; then carry the tracing-point along the straight- 
edge, A K, which is parallel to the metal groove, until the record- 
wheel shows the same reading as at the instant of starting : 
this latter distance is the length of the mean ordinate. 

38. Calibration of the Planimeter. — In order to ascertain 
whether the instrument is accurate and graduated correctly, it 
is necessary to resort to actual tests to determine the character 
and amount of error. 

It is necessary to ascertain: I. If the same readings are 
given by different portions of the record-wheel. 2. Whether 
the position of the. vernier is correct, and agrees with the con- 
stants tabulated or marked on the tracing-arm. 3. Whether 
the scale of the record-wheel is correct, and agrees with the 
constants marked on the tracing-arm. 

These tests are all made by comparing the readings of the 
instrument with a definite and known area. To obtain a defi- 
nite area, a small brass or German-silver rule, shown at Z, Fig. 
11, is used; this rule has a small needle-point near one end, 
and a series of small holes at exact distances of one inch or 
one centimeter from the needle-point. To use the rule the 
needle-point is fixed on a smooth surface covered with paper, 
the planimeter is set with its tracing-point in one of the holes 
of the rule, and the pole-point fixed as required for actual use. 
With the tracing-point in the rule describe a circle, as shown 
by the dotted lines (Fig. 17) around the needle-point as a 
centre. Since the radius of this circle is known, its area is 
known ; and as the tracing-point of the planimeter is guided in 
the circumference, the reading of the record-wheel should give 
the correct area. 



§38.] 



APPARATUS 



53 



The method of testing is illustrated in Figs. 17, 18, 19, and 
20. Figs. 17 and 18 show the method with reference to the 
polar planimeter; Figs. 19 and 20 show the corresponding 
methods of testing the rolling-planimeter. In Figs. 17 and 19 
P is the position of the pole, B the pole-arm, and A the tracing- 
arm. In Figs. 18 and 20 B is the axis of the rollers and A is 
the tracing-arm. 

First Test. This operation, see Figs. 17 and 18, consists 
in locating the planimeters as shown, and then slowly and 




Fig. 17. 



carefully revolving so as to swing the check-rule as shown 
by the arrow. Take readings of the vernier at initial point, 
and again on returning to the starting-point : the difference of 
these readings should give the area. Repeat this operation 
several times. 

The instrument is now placed in the position shown in 
Figs. 19 and 20 when the circle K appears on the right-hand 
side of the tracing-arm A, and the passage of the tracer takes 
place in exactly the same way. 

If the results obtained right and left of the tracing-arm be 
equal to one another, it is clear that the axis ab of the measur- 
ing-wheel is parallel to the tracing-arm, and, this being so, the 
second test may now be applied. But if the result be greater 
in the first case, that is to say, when the circle lies to the left 



54 



EXPERIMENTAL ENGINEERING, 



[§38. 



of the tracing-arm, the extremity a of the axis of the measur- 
ing-wheel must be further removed from the tracing-arm ; if it 
be less, that extremity must be brought nearer to the tracing- 
arm. 

Second Test. The tracing-arm is adjusted by means of the 
vernier on the guide and by means of the micrometer-screw, 
in accordance with the formulae for different areas; it then is 
fixed within the guide by means of the binding-screw. The 
circumference of circles of various sizes are then travelled over 




Fig. 20. 



with the check-rule, and the results thus obtained are multi- 
plied into the unit of the vernier corresponding to the area 
given for that particular adjustment by the formula. The fig- 
ures thus obtained ought to be equal to the calculated area of 
the circles included by the circumferences. If the results ob- 
tained with the planimeter fall short of the calculated areas to 

the extent of — of those areas, the length of the tracing-arm, 

that is to say, the distance between the tracer and the fulcrum 

of the tracing-arm, must be reduced to the extent of - of that 

length ; in the opposite case it must be increased in the same 
proportion. The vernier on the guide-piece of the tracing-arm 
shows the length thus defined with sufficient accuracy, usually 



§390 



APPARA TUS. 



55 






in half-millimeters, or about fiftieths of an inch, on the gauged 
portion of the arm. 

In order to test the accuracy of the readings according to 
the two methods just described, some prefer the use of a 
check-plate in lieu of the check-rule. The check-plate is a cir- 
cular brass disk upon which are engraved circles with known 
radii. 

It is advisable to apply the second test also to a large dia- 
gram drawn on paper and having a known area. 

The instrument having been found correct or its errors de- 
termined, it may now be used with confidence. 

The following form is used to record the results of the test : 

Calibration of Planimeter 189. 

by Dia. register- wheel, in . . . 

Formula of Instrument Length of arms, pole to pivot, in . . . 

Pivot to register-wheel, in. . . . Pivot to tracing-point, in. . . 

In Roller Pla. radius roller, in. . . . Pitch radius Gears, No. I. . . .No. II ... . 



COMPARISON WITH STANDARD. 



Area. 


Mean Ordinate. 


No. 


Inst. Reading. 



Difference from 
Mean. 

e 


€* 


Inst. Reading. 



Difference from 
Mean. 

e 


e* 
















Mean 















Mean error of one observation, ± \/2e* ■*- (n — 1) in area. . . ., in ordinate. . .in. 
Mean error of result, ± j/2e 2 -*- n{n — 1) in area. . ., in ordinate. . .in. 
Probable error of one obs., ± 0.67 tflZe 1 -*-(» — 1) in area. . . ., in ordinate. . . in. 
Probable error of result, ± 0.67 yjS* 2 -*-«(«— 1) in area in ordinate ... in. 



39. Errors of Different Planimeters.— Professor Lorber, 
of the Royal Mining Academy of Loeben, in Austria, made 



56 



EXPERIMENTAL ENGINEERING. 



[§39 



extensive experiments on various planimeters, with the results 
shown in the following table : 







The error in one passage of the tracer amounts on an average to 
the following fraction of the area measured by — 


Area in— 


The ordinary 
Polar Plan- 
imeter Unit 
of Vernier: 

10 sq. mm. = 
.015 sq. in. 


Stark's Linear 
Planimeter 
Unit of Ver- 
nier: 
1 sq. mm. = 
.015 sq. in. 


Suspended 
Planimeter 
Unit of Ver- 
nier: 

1 sq. mm. = 
.0015 sq. in. 


1 

Rolling Planimeter — 




Unit of Ver- 
nier: 
1 sq. mm. = 
.0015 sq. in. 


Unit of Ver- 


Square 
cm. 


Square 
inches. 


nier: 
.1 sq. mm. = 
0001 sq. in. 


IO 

20 

50 

IOO 

200 

300 


i-55 
3.10 

7.75 
15-50 
31.00 
46.50 


4% 

12V? 


TWO" 
TsV? 

TSsT 


T2J 
TAX 

ITFO 
7T6T 

ttVs- 

TTFT 


4? 

Tow 

2 0" 

33V3 

BTffff 

ToW 


1000 
20 0". 
3006 

swo" 

YW¥ 
10000 



The absolute amount of error increases much less than the 
size of the area to be measured, and with the ordinary polar 
planimeter is nearly a constant amount. 

The following table is deduced from the foregoing, and 
shows the error per single revolution in square inches: 







Error in one passage of the tracer in square inches — 


* Area in— 


Polar Planim- 
eter Unit of 
Vernier: 
10 sq. mm. = 
.015 sq. inches. 


Suspended Plan- 
imeter Unit of 
Vernier: 
1 sq. mm. = 
.0015 sq. inches. 


Rolling Planimeter— 




Unit of Vernier: 

1 sq. mm. = 
.0015 sq. inches. 




Square 
cm. 


Square 
inches. 


Unit of Vernier: 

.1 sq. mm. = 
.0001 sq. inches. 


IO 

20 

50 

IOO 

200 
300 


1-55 
3-IO 

7.75 
I5-50 
31.OO 
46.50 


0.0207 
O.0206 
0.022I 
O.0227 
O.0243 


O.OO25 
O.OO28 
O.OO31 
O.OO35 
O.OO43 
O.OO49 


lOHOO CO O CO 
N CO CO rtvO in 

8 8 8 8 8 8 
6 6 6 6 6 6 


O.OOI55 
O.OOI58 
O.OO258 
O.OO31O 
O . OO403 
O . 00465 



These errors were expressed in the form of equations, as 
follows, by Professor Lorber. Let / equal the area corre- 



§40.] 



APPARA TVS. 



$7 



sponding to one complete revolution of the record-wheel ; let 
dF be the error in area due to use of the planimeter. Then 
for the different planimeters we have the following equations : 



Lineal planimeter, 
Polar planimeter, 
Precision polar planimeter, 
Suspended planimeter, 
Rolling planimeter, 



dF = 0.0008 1/+ 0.00087 VFf\ 
dF = 0.001 26/+ 0.00022 s Ff\ 
dF= 0.00069/ +0.00018 \~Ff) 
dF = 0.0006/ + 0.00026 VFf 
dF =0.0009/ +0.0006 V~F/, 



40. Moment Planimeters much more complicated than those 
described have been made for special purposes, of which we 
may mention Amsler's mechanical integrator for finding the 
moment of inertia, and "Coradi's" mechanical integraph for 
drawing the derivity of any curve, the principal curve being 
known, thus giving a graphic representation of moment. 



ni^iiniiimijim'n[injTii]nifnijiinnipnrii 



r,T i 1 



■ ! ! 



1 1 1 



T 



mm 



i|tn|iiijuiiN[wpiijuj|ni|iii|iii^ 



S 



Fie 21.— Vernier Caliper. 



40. Vernier Caliper. — This instrument consists of a slid- 

ing-jaw, which carries a vernier, and may be moved over - 
fixed scale. The form shown in Fig. 21 gives readings to ^„ 
inch on the limb, and ^ this amount or to one-thousandth of 



58 EXPERIMENTAL ENGINEERING. |_§ 4: 

an inch on the vernier. The reading of the vernier as it is 
shown in the figure is 1.650 from the scale, and 0.002 on the 
vernier, making the total reading 1.652 inches. This instru- 
ment is useful for accurate measurements of great variety ; the 
especial form shown in the cut has a heavy base, so that it will 
stand in a vertical position and may be used as a height-gauge. 
To use it as a caliper, the specimen to be measured is placed 
between the sliding-jaw and the base ; the reading of the vernier 
will give the required diameter. 

41. The Micrometer. — This instrument is used to meas- 
ure small subdivisions. It consists of a finely cut screw, one 
revolution of which will advance the point an amount equal to 
the pitch of the screw. The screw is provided with a gradu- 
ated head, so that it can be turned a very small and definite 
portion of a revolution. Thus a screw with forty threads to 
the inch will advance for one complete revolution -fa of a n 
inch, or 25 thousandths. If this be provided with a head sub- 
divided to 250 parts, the point would be advanced one ten- 
thousandth of an inch by the motion sufficient to carry the 
head past one subdivision. 

The micrometer is often used in connection with a micro- 
scope having cross-hairs, and in such a case represents the 
most accurate instrument known for obtaining the value of 
minute subdivisions; it is also often used in connection with 
the vernier. The value of the least reading is determined by 
ascertaining the advance due to one complete revolution, and 
dividing by the number of subdivisions. The total advance of 
he screw is equal to the advance for one revolution multiplied 
jy the number of revolutions plus the number of subdivisions 
multiplied by the corresponding advance for each. 

The accuracy of the micrometer depends entirely on the 
screw which is used. 

Accuracy of Micrometer-screws. — The accuracy attained in 
cutting screws is discussed at length by Prof. Rogers in Vol. V. 
of Transactions of American Society of Mechanical Engineers, 
from which it is seen that while no screw is perfectly accurate; 
still great accuracy is attained. The following errors are those 



§42.] 



APPARA TUS. 



59 



in one of the best screws in the United States, expressed in 
hundred-thousandths of an inch, for each half-inch space, 
reckoned from one end. 



CORNELL UNIVERSITY SCREW. 

Total Errors in Hundred-thousandths of an Inch. 



No. of Space. 


Total Error. 


No. of Space. 


Total Error. 


No. of Space. 


Total Error. 


o 


O 


12 


- 4 


24 


-8 


I 


+ 6 


13 


- 7 


25 


-7 


2 


+ 8 


14 


- 9 


26 


-7 


3 


+ 9 


15 


- 7 


27 


-9 


4 


+ 7 


16 


— IO 


28 


-9 


5 


+ 9 


17 


— ii 


29 


-7 


6 


+ 7 


18 


— ii 


30 


— 7 


7 


+ 4 


19 


— IO 


31 


-6 


8 


+ 5 


20 


— IO 


32 


-7 


9 





21 


- 9 


33 


-7 


IO 


— i 


22 


— ii 


34 


-3 


ii 


— 2 


23 


— IO 


35 
36 


— 2 




A recent investigation made by the author of the errors in 
the ordinary Brown and Sharpe micrometer-screw, failed to 
detect any errors except those of observation, which were 
found to be about 4 hundred-thousandths of an inch for a 
distance equal to three-fourths its length. The errors in the 
remaining portion of the screw were greater ; the total error 
in the whole screw being 12 hundred-thousandths of an inch. 
As the least reading was one ten-thousandth, the screw was in 
error but slightly in excess of the value of its least subdivision. 
In another screw of the same make the error was three times 
that of the one described. 

42. Micrometer Caliper consists of a micrometer-screw 
shown in Fig. 22, which may be rotated through a fixed nut. 
To the screw is attached an external part or thimble y which 
has a graduated edge subdivided into 25 parts. The fixed nut 
is prolonged and carries a cylinder, termed the barrel, on which 
are cut concentric circles, corresponding to a scale of equal parts, 
and a series of parallel lines, which form a vernier with refer* 



6o 



EXPERIMENTAL ENGINEERING. 



■ [§ 42. 



ence to the scale on the thimble, the least reading of which is 
one tenth that on the thimble. If the screw be cut 40 threads 
per inch, one revolution will advance the point 0.025 inch ; and 
if the thimble carry 25 subdivisions, the least reading past 
any fixed mark on the barrel would be one thousandth of an 
inch. 

By means of the vernier the advance of the point can be 
read to ten-thousandths of an inch. Thus in the sketches of 




Fig. 22.— Micrometer Caliper. 



the barrel and thimble scales in Fig. 16 the zero of the vernier 
coincides in the upper sketch with No. 7 on the thimble ; but 
in the lower figure the zero of the vernier has passed beyond 7, 
and by looking on the vernier we see that the 3d mark coincides 
with one on the thimble, so that the total reading is 0.007 + 
O.0003, which equals 0.0073 inch. 

This number must be added to the scale-reading cut on the 
barrel to show the complete reading. The principal use of the 
instrument is for measuring external diameters less than the 
travel of the micrometer-screw. 

The Sweet Measuring-machine. — The Sweet measuring- 
machine is a micrometer caliper, arranged for measuring larger 
diameters than the one previously described. The general 



§42-] 



APPARA TUS. 



61 



form of the instrument is shown in Fig. 23. The micrometer- 
screw has a limited range of motion, but the instrument is fur- 
nished with an adjustable tail spindle, which is set at each 




Fig. 23; —Sweet's Measuring-machine. 



observation for distances in even inches, and the micrometer, 
screw is used only to measure the fractional or decimal parts 
of an inch. The instrument is furnished with an external 




scale, graduated on the upper edge to read in binary fractions 
of an inch, and on the lower edge to read in decimals of an 
inch ; this scale can be set at a slight angle with the axis to 
correct for any error in the pitch of the micrometer-screw. 




62 EXPERIMENTAL ENGINEERING. |_§ 43. 

The graduated disk is doubly graduated ; the right-hand grad- 
uations corresponding to those on the lower side of the scale. 
The scale and graduated disk is shown in Fig. 24, and the read- 
ings corresponding to the positions shown in the figure are 
O.6822, the last-number being estimated. 

The back or upper side of the scale, and the left-hand disk, 
are for binary fractions, the figures indicating 32ds. Fig. 25 
shows the arrangement of the figures. 
Beginning at o and following the line of 
chords to the right, the numbers are in 
regular order, every fifth one being counted, 
and coming back to o after five circuits. 
This is done to eliminate the factor five 
from the ten-thread screw. In Fig. 24 the 
portion to the left of o in Fig. 25 is seen. 
The back side of the index-bar is divided only to i6ths, the 
odd 32ds being easily estimated, as this scale is simply used for 
a "finder;" thus: In the figure the reading line is very near 
the ^ mark, or six 32ds beyond the half-inch. This shows 
that 6 is the significant figure upon this thread of the screw. 
The other figures belong to other threads. The figure 6 is 
brought to view when the reading line comes near this division 
of the scale. Bring the 6 to the front edge of the index-bar, 
and the measurement is exactly -^ without any calculation. 
Thus every 32d may be read, and for 64ths and other binary 
fractions take the nearest 32d below and set by the interme- 
diate divisions, always remembering that it requires five spaces 
to count one. 

43. The Cathetometer. — This instrument is used exten- 
sively to measure differences of levels and changes from a 
horizontal line. Primarily it consists of one or more telescopes 
sliding over a vertical scale, with means for clamping the tele- 
scope in various positions and of reading minute distances. 
The one shown in the engraving (Fig. 26) consists of a solid 
brass tripod or base supporting a standard of the same metal, 
the cross-section of which is shown at different points by the 
small figures on the left. A sliding-carriage upon which is 



§43-] 



APPARA TVS. 



63 



secured the small levelling instrument, and whic has also a 
vernier scale as shown, is balanced by heavy lead weights, sus- 




Fig. 26. — Thk Cathetometer. 



pended within the brass tubes on either side by cords attached 
to the upper end of the carriage, and passing over the pulleys 



64 EXPERIMENTAL ENGINEERING. [§ 43- 

shovvn at the top of the column. The column is made ver- 
tical by reference to the attached plumb-line. 

The movable clamping-piece below the carriage is fixed at 
any point required, by the screw, shown at its side, after which 
the telescope can be raised or lowered by rotating the micro- 
meter-screw attached to the clamp. The telescope is provided 
with cross-hairs, which can be adjusted by reversing in the 
wyes and turning 180 degrees in azimuth. The vertical scale 
is provided with vernier and reading-microscope. 

Aids to Computation — Graphical methods for multiply- 
ing or dividing are usually given in treatises on geometry and 
aie often sufficiently accurate for the required results. Tables 
of logarithms and of products often save much labor. The 
Rechentafeln by A. L. Crelle of Berlin gives one million 
products and will be found of much value in multiplication 
and division. A very excellent logarithmic table has recently 
been issued by Prof. G. W. Jones, Ithaca, N. Y. 

Computation Machines Several very excellent ma- 
chines for multiplying and dividing are now made, which 
give accurate results to from 14 to 17 places. Of these we may 
mention, as moderate in price and of perfect accuracy, the 
calculating machine of George B. Grant of Boston; the 
Brunsvega by Grimme-Natlis & Co.. Brunswick, Germany, 
and the Comptometer, made by the Comptometer Co. of 
Chicago. Slide-rules of compact form but with with scales 
40 feet in length, as designed by Thatcher or Fuller, can also 
be obtained of the principal stationers. 

The processes of arithmetical calculation are almost entirely 
mechanical and involve no reasoning powers, yet they are of 
utmost importance in connection with experimental work. 
Unless the observations of the experiment are correctly 
recorded and the necessary calculations for expressing the 
result made accurately, the experimental work will either be of 
no value, or, what is worse, positively misleading. For these 
reasons mechanical methods of computation, which involve at 
best small errors of known magnitude, are to be adopted when- 
ever possible in reducing engineering experiments. 



§43-] APPARATUS. 65 

The calculating machine is of especial value, since if the 
mechanical processes are correctly performed the results will 
be given with accuracy for the number of places within limits 
of the machine. Numerous calculating machines have been 
designed, the most noted of which is the " difference engine " 
designed by Babbage in 1822 and on which the English Govern- 
ment expended more than $85,000 without bringing it to per- 
fection. The first practical machine which accomplished any- 
thing worthy of permanent record was invented by Thomas de 
Colmar in 1850, and since that time numerous others, designed 
on similar lines, have appeared, of which should be mentioned 
those invented by Tate, Burkhardt, Grant, Baldwin, and 
Odhner. The Grant machine, developed from 1874 to 1896, 
has now reached a high degree of perfection, and its price is 
within the reach of any engineering laboratory. The Odhner 
or Brunsvega, referred to above, was shown at the World's Fair 
in 1893, and differs from the Grant principally in the arrange- 
ment of parts, in the fact that, as now sold, it possesses an 
index or counter to register the multiplier during the process 
of multiplication. The Grant machine will on special order be 
fitted with this appliance ; its mechanism is much superior to 
that of the foreign instrument, and it is operated with less labor 
and noise. 

In both machines, the result is read on a series of wheels 
arranged on the same axis and so connected that ten revolu- 
tions of one of lower denomination are required for one of the 
next higher, etc., these wheels being readily and simultaneously 
set at zero. The numbers to be united are engraved on a key- 
board. By setting a lever opposite any number and turning a 
crank once, the sum will appear on the result-wheels ; by turning 
the crank twice, the result-wheels will show twice the sum, etc. 
The number keyboard can be shifted several places, so that it 
is possible to multiply by numbers of any denomination, by 
less than ten revolutions of the crank. Subtraction is per- 
formed by starting with the larger number on the result-wheel 
and the smaller number on the keyboard and revolving the 
crank in the opposite direction from that required for addition. 



66 EXPERIMENTAL ENGINEERING. [§ 43. 

Division is computed as a sort of continued subtraction, and is 
a complicated operation. The machine is readily worked as a 
difference engine, thus permitting its use for computing com- 
plicated tables. 

A trial made in the U. S. Coast Survey of the relative ra- 
pidity and accuracy of the Grant calculating machine and a 
seven-place table of logarithms, in multiplying seven figures by 
seven figures and retaining seven figures in the result, showed the 
average time of multiplication with the machine as 56 seconds, 
and with logarithms 157 seconds; the number of errors in 100 
trials, with the machine 7, with logarithms 12. A trial made 
at Sibley College showed more favorable for the machine, 
probably because the observers were not as expert with loga- 
rithms. 



STRENGTH OF . MATERIALS. 



CHAPTER III. 

GENERAL FORMULAE. 

In this chapter a statement is made of the principal for- 
mulae required for the experimental work in " Strength of 
Materials." The full demonstration of these formulae is to be 
found in "Mechanics of Engineering," by I. P. Church; 
" Strength of Materials," by D. V. Wood ; " Materials of Con- 
struction," by R. H. Thurston: N. Y., J. Wiley & Sons. 

44. Object of Experiments. — The object of experiments 
relating to the " Strength of Materials " is to ascertain, firstly, 
the resistance of various materials to strains of different char- 
acter; secondly, the characteristics which distinguish the 
different qualities, i.e., the good from the bad ; thirdly, experi- 
mental proof of the laws deduced theoretically; fourthly, 
general laws of variation, as dependent on form, material, or 
quality. 

The following methods of testing are ordinarily employed : 
(1) by tension or pulling ; (2) by compression ; (3) by trans- 
verse loading ; (4) by torsion ; (5) by impact ; (6) by repeated 
loading and unloading, or fatigue. 

45. Definitions. — Stress is the distributed force applied to 
the material ; it may be internal or external. 

Stress is of two kinds, normal or direct, and shearing or 
tangential, the latter force acting at right angles to the first. 
A direct stress on an element is always accompanied by a 
shearing stress, which tends to move the particles at right 

67 



68 EXPERIMENTAL ENGINEERING. L§ 45* 

angles to the line of action of the force. This is well shown in 
the simple break by tension, in which case the particles are not 
only pulled apart, but they are moved laterally, since the break 
is accompanied with an elongation of the original specimen, 
and a corresponding reduction in area of the cross-section. 

Strain is the distortion of the material due to the action of 
the force, and within the limits of elasticity is proportional to 
the stress. 

Each stress produces a corresponding strain. 

Elasticity is the property that most materials have of re- 
gaining their original form when the forces acting on them are 
removed. This property is possessed only to a limited extent, 
and if the deformation or strain exceeds a certain amount, the 
material will not regain its original form. 

The critical condition beyond which the body cannot be 
strained without a permanent distortion or set is termed the 
elastic limit ; this point is gradually reached in most materials, 
and is indicated by an increase in the increment of strain due 
to a constant increment of stress. 

Rigidity or stiffness is the property by means of which 
bodies resist change of form. 

The coefficient of ultimate strength is the number of pounds 
per square inch required for rupture, and is obtained by calcu- 
lation from the known area and actual breaking-load. The co- 
efficient of strength at the elastic limit is the number of pounds 
per unit of are? acting upon the material when a failing in 
strength is shown by an increased increment of distortion for 
an equal increment of load. 

The resilience is the potential energy stored in the body, 
and is the amount of work the material would do on being re- 
lieved from a state of stress. Within the elastic limit, it is the 
work done by the force acting on the body, and is evidently 
equal at any point to the product of one half the load, into the 
distortion of the piece, this latter being the space passed 
through. The elongation is the total relative strain ; it is 
usually expressed in percentage of the full length, and is 
calculated for the point of rupture. In connection with 






§ 4-6-] STRENGTH OF MATERIALS— GENERAL FORMULAE. 69 

this should be measured the reduction of area of cross-sec- 
tion. The modulus of elasticity is the ratio of the stress per 
unit of area to the deformation per unit of length. The 
modulus of rigidity is the amount of tangential stress per 
unit of area, divided by the deformation it produces, expressed 
in angular or 71 measure. The maximum load is usually greater 
than the load at rupture. 

The safe load must always be less than the load at the 
elastic limit, and is usually taken as a certain portion of the 
ultimate or breaking load. The ratio of the breaking-load to 
the safe load is termed a factor of safety. 

The different kinds of stress, consequently the different 
kinds of strain produced, are : Longitudinal, divided into tension 
and compression ; Transverst, irto shearing and bending ; and 
Twisting or Torsional. 

46. Strain-diagrams are diagrams which show the rela- 
tions which the increments of strain bear to the stress. If the 
strain-diagrams of several specimens be drawn on the same 
sheet, the relative values of stress and of strain at elastic limit 
and at breaking can be determined by inspection. Within 
the elastic limit the diagram will be a straight line. 

Strain-diagrams are constructed (see Article 19, p. 20) by lay- 
ing off the strain on the horizontal axis to a scale that is readily 
apparent to the eye, and the corresponding loads as ordinater 
to a convenient scale, as 3000 or 5000 pounds per inch : a curve 
drawn through the extremities of these various ordinates will 
be the strain-diagram. When no part is perfectly elastic, as in 
cast-iron or rubber, no portion of the curve will be straight. 

The general form of the strain-diagram, as drawn auto- 
graphically, is shown in Fig. 27. In this diagram the strain is 
represented by distances parallel to OX, the stress as a certain 
number of pounds per inch parallel to OY. For a short dis- 
tance from O to A the diagram is a straight line, showing that 
the increments of strain and stress are uniform; at A there is 
a sudden increase in the strain, without a marked increase in 
load, shown by the curved line A to B. The point A is often 
spoken of as the yield-point. In most of the ductile materials 



JO 



EXPERIMENTAL ENGINEERING. 



[§47- 



this sudden increase of strain is accompanied with an apparent 
reduction of stress, as shown by the curve from B to C. This 
reverse curvature is often well marked on curves taken auto- 
matically, and is probably due to the fact that the increase in 



Fig. 27. — The Strain-diagram. 



strain is so great that the scale-beam of the machine falls until 
the stress is increased. The curve then continues to rise, reach- 
ing its maximum position at Z\ and falling soon after when 
the specimen breaks, as shown at E. 

47. Viscosity or Plasticity. — This is the term applied to 
denote the change of form or flow that results from the appli- 
cation of stress for a long time. It is the result of internal 
molecular friction, and the resistance exerted is proportioned 
to the rapidity of the change. The definition of viscosity is 
given by Maxwell (see Theory of Heat) as follows : " The vis- 
cosity of a substance is measured by the tangential or shearing 



§ 47-] STRENGTH OF MATERIALS— GENERAL FORMULA. J I 

force on the unit of area of either of two horizontal planes at 
the unit of distance apart, one of which is fixed, while the 
other moves with the unit of velocity, the space between being 
filled with the viscous substance." 

Let the substance be in contact with one fixed plane and 
with one plane moving with the velocity v\ denote the dis- 
ta nee between the planes by c. Let F be the coefficient of 
sliearing-force, or the force per unit of area tending to move 
the substance parallel to either plane. Let fx be the coefficient 
of viscosity. 

Then we have 

F =% •• « 

If we let b = the breadth and a the length of the plane 
and R the total force acting, 

R = abF. 
Hence 

_cF _cR 

^~ v ~~ vab° 



When c, a, and b each equal unity, 

t* = R. 



If R is the moving force that would generate a certain velocity 
?' in the mass M in time /, R will equal Mv -*- /; from which 



Mvc 



a/1 of which quantities may be determined by experiment 



EXPERIMENTAL ENGINEERING. 



[§49- 



48. Notation. — The notation used is the same as that in 
Church's "Mechanics of Engineering," and is as follows: 



Quantity. 



Load applied 

Load per square inch 

Moduli of tenacity 

" " compression 

" " shearing 

Total elongation 

Increment of elongation. . . . 

Relative elongation 

Resilience 

Bending-moment , 

Relative shearing distortion. 

Transverse load — total 

Transverse shear 





Symbol. 


Maximum 


Breaking- Elastic 


Load. 


Load. 


Limit. 


Ptn 


P 


P" 


Pm 


P 


t", 


T m 


T 


T" 


C»t 


C 


C" 


2>m 


S 


S" 


X m 


X 


X" 


AX m 


AX 


AX" 


Gm 


€ 


e" 


Um 


u 


U" 


M m 


M 


M" 




8 


8" 


w m 


W 


W" 


/« 


J 


J" 



Safe 
Limit. 



P' 

* r 

a 
s* 

X' 

AX' 

e' 

U' 

M' 

8' 

W 

f 



Tension. Compression. Shearing, 
Modulus of Elasticity Et E c E s 

Area sq. inches F 

Length, " / 

Factor of safety n 

Ordinary moment of inertia / 

Polar moment of inertia Ip 

Maximum fibre-distance .e 

49. Formulae for Tensile Strength. (Church's Mechanics, 
pp. 207-221.) — Since in tension the stress is uniformly distrib- 
uted, we have 

P=FT; (2) 

P=r> (3) 

X 



€ = 



(4) 



The modulus of elasticity by definition equals the load per 
square inch divided by the strain per inch of length, within the 
elastic limit. Hence 

p P__P}__ pl 

X - X - FX " * ° * * 

7 



K. — iL — t- _ £1 _ 



(5) 



§ 5I-] STRENGTH OF MATERIALS— GENERAL FORMULAE. 73 

Resilience U = mean force X total space = \P"X" = 
\P"e"l = \T"e"FL But Fl equals the volume V. 

.\ U= : kT"e"V=\P"e"L . . . . (6) 

50. Modulus of Elasticity from Sound emitted by a 
Wire. — Let / equal the length of the wire, d equal its specific 
gravity, n equal the number of vibrations per second, v equal 
the velocity in feet per second. 

Determine the number of vibrations by comparing the 
sound emitted, caused by rubbing longitudinally, with that 
made by the vibration of a tuning-fork. In this manner de- 
termine the note emitted. The number of vibrations per 
second can be found by consulting any text-book devoted to 
acoustics. 

We shall have finally 

v = 2nl) 



also 



'Eg 



W§ 



from which 






This result usually gives a larger value by one or two per 
cent than that obtained by tension-tests, owing to the viscosity 
of the body. 

51. Formulae for Compression-tests. — The compression- 
tests are of value in determining the safe dimensions of mate- 
rial subject in use to a crushing or compressive stress. Nearly 



7 A EXPERIMENTAL ENGINEERING. [§ 5 1. 

all bearings in machinery, a portion of the framework, the 
connecting-rod of an engine, during some portion of a revo- 
lution, are illustrations of common occurrence, of members 
strained by compression. Columns and piers of buildings, 
masonry-walls, are familiar illustrations in structures. 

The subject is naturally divided into two heads, the strength 
of short specimens and the strength of long specimens, since 
the strain is manifestly different in each case. 

Short Pieces, or those in which the length is not more than 
four diameters, yield by crushing, and the force acts uniformly 
over each square inch of area, so that formulae similar to those 
used in tension apply. (For notation see article 48, page 62.) 
We have 

(8) 
(9) 



(10) 

Resilience U. = iP"X" = iP"e"/=iC"e"F/. . . (n) 

The compression-strain is accompanied with a shearing- 
strain acting at right angles to the specimen equal to P sin a 
cos a, being a maximum when a = 45 . Hence, brittle 
materials tend to fly to pieces at that angle, leaving two pyra- 
mids with facing points. 

Long Pieces, in which the length equals ten or twenty diam- 
eters, yield by bending on the side of least resistance. 

Rankine's formula is most used for this case (Church's 
Mechanics, page 374). 

Breaking-load for flat ends, 

P i= FC+(i+P F ).. . c . . . (12) 



p 

P, — FC: fi — -^.. . * 




e — -r • --. 


/ 

p pi PI 
n < — e - A - FX' * 


e e • 






§ 51.] STRENGTH OF MATERIALS— GENERAL FORMULAE. 75 

Breaking-load for round-ended or two-pin column, 



I2aj 



Breaking-load for one round end and one square end orpin 
and square end, 



>, = FC+{i+%pQ. ....... (12 



9 /£ 



*) 



Value of Coefficients as given by Rankine. 



Coefficients. 


Cast-iron. 


Wrought-iron. 


Timber. 


€ in pounds per sq. inch 


80000 
I -T- 6400 


36000 
I -7- 36000 


7200 
I -T- 3000 





Notation in above Formulas, 
F = area in square inches. 
/= length in inches. 
K = radius of gyration. 
K 2 — I -1- F. See page 7% for values of /. 
In case the modulus of elasticity is required, Enter's for- 
mula should be used ; in this 

p: r = eitz 1 -f. i m 

for round-ended columns, in which l" = / — - K 9 



In' 



(13) 



For a column with flat ends, 

P i " = 4 El7r> + l">; l" = l-Ti. . . .(13a) 

For a column with one pin or round end and the other end 
square, 

/>" = \EIn* -j- 1"\ /" = /-*.. . . . (13$) 

Euler's formula has only been approximately verified by 
experiment. 



76 EXPERIMENTAL ENGINEERING. [§ 52. 

52. Transverse Stress. — Theory. — In case of transverse 
stress the force, or a component of the force, is applied at right 
angles to the principal dimensions of the material. The 
material is generally in the form of a beam, and the strains 
produced make the beam assume a concave form with refer- 
ence to the direction of the force applied. The result of this 
is a compression of the fibres nearest the force, and a corre- 
sponding elongation of those farthest away. The fibres of 
the beam not strained or deformed by any longitudinal force 
lie in what is called the neutral axis. The curve which the 
neutral axis assumes due to the forces acting is termed the 
elastic curve. 

The weight carried tends to rupture the beam at right 
angles to the neutral axis ; this stress is equal to the resultant 
force acting at any point, and is termed the transverse shear. 
In addition to this there is a shearing-force tending to move the 
fibres of the beam with reference to each other in a longitudi- 
nal direction, which is termed parallel shear; this force is a 
small one compared with the other forces, and for that reason 
is difficult to measure experimentally. 

Formula. — In this case the external load is applied with an 
arm, and tends to produce rotation ; the result is termed the 
Moment of Flexure or Bending-moment, which is denoted by M. 

The internal moment of resistance is equal to pT -r- e, in 
which p equals the intensity of. strain on the outermost fibre 
of the piece, I equals the moment of inertia, e equals the 
distance of the outermost fibre to the neutral axis. Since 
these moments must be equal, we have 

M = pf-r-e, . (14) 

which formula may be used for strength. We also have 

EI+p = M, (15). 



which may be used for flexural stiffness (Church's Mechanics, 

page 250), in 
(approximately). 



d*y 
page 250), in which p = radius of curvature = 1 -=- ~t-\ 



§52.] STRENGTH OF MATERIALS— GENERAL FORMULAE. 77 

Hence 

±EI % = M ' < 16 ) 

which is the differential equation of the elastic curve. 

To find the external moment M, consider the beam as a 
lever, subject to action of forces, only on one side of the free 
section. If we consider A as the amount carried by any abut- 
ment, or the resistance acting at one end, x the distance to the 
free section, W the weight of any load or loads between the 
abutment and the free section, and x' the distance of the point 
of centre of gravity of these loads to the free section, then by 
the principles of moments we have the general equation 

M=Ax- Wx'. ...... (17) 

In problems relating to the elastic curve assume the general 
differential equation 

Find the numerical value of M expressed in terms of one 

dimension of the beam as variable. Thus, as above, M = Ax 

— Wx. Select the origin of co-ordinates in such a position 

that the constants of integration can be determined. Then 

dy 
integrate. The first integration will give the value of — - or 

the tangent of the elastic curve ; the second integration will 
give j, the ordinate to the elastic curve. 

The parallel shear is maximum in the neutral axis, and de- 
creases either way proportionally to the ordinates of a parabola. 

The value of the parallel shear per unit of section in the 
neutral axis is 

area above neu- \ ( the distance of its ] 

tral axis (or VxK centre of gravity >; (18) 
below) ) I from that axis, j 




78 



EXPERIMENTAL ENGINEERING. 



[§52. 



in which I is equal to the moment of inertia, J the total trans- 
verse shear, and b a the thickness of beam in the neutral axis. 

In the ordinary cases of shearing-forces, such as act on 
rivets or pins, the intensity is uniform ; this case is considered 
later. 

The following tables of moments of inertia, of transverse 
loads, and of external moments will be useful in working up 
the results of the experiments. 

TABLE NO. I. 

Moments of Inertia. 



Rectangle, width b, depth h 

Hollow rectangle, symmetrical 

Triangle, width = b, height = h.. . 

Circle of radius r. . 

Ring of concentric circles 

Rhombus h — vertical diagonal. . . 

Square with side (b) vertical 

Wat 45° 



Ordinary Moment. 
/. 



tV^ 3 

A** 



3f2 



b i 



h* 



Polar Moment. 



AW + A') 



A** 



Max. Fibre 
Dist. 



r 

\b 
\b^2 



TABLE NO. II. 
Formulas for Transverse Loads. 



Deflection = d. 

Maximum fibre-strain /. ....... 

Safe load.. 

Coefficient R' 

Relative strength, equal length 

Relative stiffness, equal load.. . 

" " safe load. . . . 

Modulus elasticity 

Max. shear 



Cantilevers. 



With one End 
Load P -. 

Wt. of Beam 
neglected. 



EI 



Pie -h 1 
R'l -r- le 
Pie -hi 



PI* -H 3 dl 
Pa.t support 



With Uni- 
form Load. 
lV=wl. 



\WP-h El 
Wle -4- 2/ 
■*R'l -hie 
Wle -s- 2/ 



WP -h 8dl 
W at support 



Beams with Two 
Supports. 



Load P, in 

Middle. 
Wt. of Beam 

neglected. 



&PP h- EI 
Pie -4- 4/ 
4 R'l -h le 
Pie h- 4/ 



Uniform 

Load. 
W=wl. 



PI* -h 4 8*7 
\P at supp't 



&WP + E1 

Wle -h 8/ 
BR'I * le 
Wle -h 8/ 
8 

4* 

V 

5^/3-4-384^/ 

$Wa.t supp't 



§ 5 2 -J STRENGTH OF MATERIALS— GENERAL FORMULAE. 79 



a o 



o >-. o 






«= x . 

•2 3 Js 






s 



II- 

H Ho -f- 

1 ' & 



H» H 



^ ^ ^ 



H 
I 

Hi M 



T^H 



■H l 



e e 



fe|' 



i ^h * hi 

.IN g | 



H H 



I I 



^ >* 



w S :.S 

M a; ! 

z a <*< 

o g .o 



3.-'° «,2 »t 

3 ^ & & 

« h» ~ ~ 



x So 

° •** £ 

§ Jo 

< ^ 



•a a> 
.22 5 



S^- 



lis 

C »* CO 



(75 
> 



6 

g || "3 m P^ 






i 0(33 



80 EXPERIMENTAL ENGINEERING. [§ 53« 

53. Moment of Inertia by Experiment. — If the body can 
be suspended on a knife-edge so that it can be oscillated back- 
ward and forward like a pendulum, its moment of inertia can be 
found as follows : First, balance the body on a knife-edge, and 
find experimentally the position of its centre of gravity; denote 
the distance of the centre of gravity from the centre of suspen- 
sion by 5. Weigh the body, and compute its mass M; denote 
its weight by W. Suspend the body on the knife-edge, and set 
it swinging through a very small arc ; find the time of a single 
vibration, by allowing it to swing for a long time and divid- 
ing by the number of vibrations. Let / equal the time in 
seconds of a single vibration or beat ; let K equal radius of 
gyration, so that MK a equals moment of inertia. 

Then, by mechanics, 



or, by reduction, 



7l 2 



*'=¥• 09) 



In this equation K is reckoned from the point of suspension, 
and the moment of inertia is the moment around the point of 
suspension. 

The moment of inertia about a parallel axis through the 
centre of gravity, may be denoted by MK C \ and we shall have 



mk; + ms 2 = mk*\ 



See Weisbach, Vol. I., page 662. 






§ 55-] STRENGTH OF MATERIALS— GENERAL FORMULAE. 8 1 
from which 

and 

MKf = M(K 2 - S 2 ). 

54. Shearing-strain. — This strain acts in a transverse 
direction, without an arm, and thus tends to produce a square 
break ; it acts uniformly over the whole section, so that 

P=SF; S = P+F. (20) 

The strain produces on the molecules of the material an 
angular distortion, which is usually expressed in n measure, or 
the linear length of the degree of distortion to a radius unity, 
and is denoted by S. 

Let p s be the stress per square inch. 

E s =p s + d. . (21) 

E s is termed the modulus of rigidity. 

The coefficient of shearing-strength S can be obtained by 
direct experiments, by using the specimen in the form of pins 
or rivets holding links together, the links being fitted to go in 
the machine like tensile specimens, and tensile force applied ; 
if the specimen is a plate, its resistance to shearing-strain can 
be found by forcing a punch through, as in compression- 
strains. The angular distortion cannot be measured directly, 
but may be determined by tests in torsion, as described. 

55. Torsion. — The strain produced by torsion is essentially 
a shearing-strain on the elements of the specimen. The effect 
of torsion is to arrange the outer fibres of the specimen into 
the form of helices, as can readily be seen by examining a test- 
piece broken by torsion stress ; each one of these fibres makes 
an angle with its original position or axis of the piece, equal 
to its angular distortion, or 6, which is expressed in n measure. 
This has the effect also of moving any particle in the surface of 



82 EXPERIMENTAL ENGINEERING. [§ 55. 

the specimen, through an angle lying in a plane perpendicular 
to the axis and with its vertex in the axis. This last angle is 
called a. Letting / equal the length of the specimen, e equal 
its radius, we have, neglecting functions of small angles, 

ea — lS, (22) 

from 

d = ea-*r L (22a) 

But since E s =p s -f- #, 

E s —p s l-^-ea\ (22b) 

from which E s , the modulus of rigidity, may be computed. 
Since the external moment of forces is equal to the internal 
moment of resistance, if we let P equal the external load, a its 
lever-arm, and I P the polar moment of inertia, we will have 

P* = (pJ p )~e, (23) 

from which 

p s = Pae-T-f p . ...... (24) 

For a circular rod of radius r 1 , 



Ia = — — , also e = y. 

2 



Let the external moment Pa. = M t . Then 






§ 57.] STRENGTH OF MATERIALS— GENERAL FORMULAE. 83 

The torsional resilience, or work done, will equal the aver- 
age load multiplied by the space, or 

U^iPjLCt. ......... (25) 

56. Modulus of Rigidity of a Wire by swinging under 
Torsion. — The transverse modulus of elasticity, or the modu- 
lus of rigidity, can be determined by hanging a heavy weight 
on the wire, and swinging it around a vertical axis passing 
through its point of suspension. Let /equal its length in feet, 
r its radius in feet, I P the polar moment of inertia of the swing- 
ing weight, t the time in seconds of an oscillation. Let E s 
be the modulus of rigidity. Then 



E < = 7^ ^ 

57. Relation of E s and E t . — Let the distortion in direc- 
tion of the stress equal e, the angular lateral distortion = 6, the 
lineal lateral distortion = m ; then 



f S\ 1 — m 
tan [45 1 = — — — = 1 — m — e, nearly. 

But since d is small, 



tan (45 ° J = 1 — 6, nearly. 



Hence, by substituting, 

S = m + e. 



Now 



E t = t and E, = il; 

e o 



84 EXPERIMENTAL ENGINEERING. [§ 58. 

Hence 

E s € € 



E t 26 2(m + e) 

In cast-iron, by experiment, Prof. Bauschinger found for 
cast-iron m = .236; hence for this case E s = 0.407 E t . 

58. Combination of Two Stresses. Intensity of combined 
Shearing* and normal Stress. — Let q be the intensity of the 
shearing-stress, which acts on the transverse section and on a 
parallel section, and let/ be the intensity of the normal stress 
on the transverse section ; it is required to find a third plane 
such that the stress on it is wholly normal, and to find r the 
intensity of that stress ; let this plane make an angle 6 with 
the transverse section. Then, from equilibrium of forces, 

(r — p) cos 6 = q sin 0, and r sin = q cos 6. 
Hence <f — r ( r —p)> 

tan 26 = 2q -7- p (27) 



r = ip± *y + i/v- • • • (28) 

58a. Twisting combined with Longitudinal Stress. — In 

a circular rod of radius r x , a total longitudinal force P\\\ the 
direction of the axis gives a longitudinal normal stress 

p 1 = P-r- area =P -r- 7tr?. 

A twisting-couple M applied to the same rod gives a shearing- 
stress whose greatest intensity 

q, = 2M t +- nr*. 

* Encyc. Britannica, art. " Strength of Materials." 



§ 59-] STRENGTH OF MATERIALS— GENERAL FORMULA?. 85 

The two together give rise to a pair of principal stresses, as 
above, 

P , /(2MV . 7^ , . 

^^iVW+K (29) 



59. Twisting combined with Bending. — This important 
practical case is realized in a crank-shaft. 

Let P be the force applied to the crank-shaft ; let R be the 
radius of the crank-shaft ; let B equal the outboard bearing, 
or the distance between the plane of revolution of the centre 
of the crank-pin and the bearing. 

If we neglect the shearing-force, there are two forces acting: 
a twisting-force M x — PR, and ben ding-moment M^ = PB. 
The stresses per unit of area on the outer fibre would be p t = 
4M 3 -r- nr? (in which r t is the radius of the crank-shaft) from 
formulae for transverse strength, and p s = 2M X -5- nr* from for- 
mula for torsion. 

Combining these as in equation (27), we find for the prin- 
cipal stress 



r = 2(M 2 ± VM? + M?) ~ nr!. 
By substituting values of M x and M % , 



r=2PiB±VB* + R')+nr!. • • . . (30) 
The greatest shearing-stress equals 



p s = 2P\ / B 2 +R*-r-nr!. (31) 

The axes of principal stresses are inclined so that 

tan 26 = M x -5- M % = R ~ B. . . . . . . (32) 



86 EXPERIMENTAL ENGINEERING. [§ 60. 

6o. Thermodynamic Relations.* — Thermodynamic theory 
shows that heat is absorbed when a solid is strained by 
opposing and is given out when it is strained by yield- 
ing to any elastic force of its own, the strength of which 
would diminish if the temperature were raised. As, for 
example, a spiral spring suddenly drawn out will become 
lower in temperature, but when suddenly allowed to draw 
in will rise in temperature. With an india-rubber band the 
reverse condition is true, which indicates that the effect of 
heat is to contract instead of to expand the rubber. From 
this theory the rise in temperature can be calculated for a- 
given strain. Thus let / equal the absolute temperature of the 
body; the elevation of temperature produced by sudden 
specific stress/ ; let e equal the corresponding strain ; /Joule's 
equivalent ; k the specific heat of the body under constant 
stress ; 6 its density. Then 

•=% <33> 

in which both *and/ are infinitesimal, or very small quantities. 
Rubber differs from other material in the relation of strain 
to stress and consequently in the direction of curvature of 
the strain diagram. While most materials show a great in- 
crease in strain after passing the elastic limit, rubber on the 
contrary shows a decrease. 



*See paper by Wm. Thomson in Philosophical Magazine 1877, also vol, 
III, page 814, ninth edition Encyc. Britannica. 



CHAPTER IV. 
STRENGTH OF MATERIALS-TESTING MACHINES. 

61. Testing-machines and Methods of Testing. — The 

testing-machines consist essentially of, fin,t, a device for weigh- 
ing or registering the power applied to rupture material; 
second, head and clamps for holding the specimen ; third, suit- 
able machinery for applying the power to strain the specimen ; 
and fourth, a frame to hold the various parts together, which 
must be of sufficient strength to resist the stress caused by 
rupture of the specimen. Machines, are built for applying 



K-a-iE 





Fig. 29.— Old Form. 



Fig. 30.— Thurston, Polmeyer. 



tensile, compressive, transverse, and torsional stresses ; they 
vary greatly in character and form ; some are adapted for 
applying more than one kind of stress, while others are limited 
to a single specific purpose. 

Ir> ^11 machines the weighing device should be accurate and 
sufficiently sensitive to detect any essential variation in the 
stress, and every laboratory should be provided with means for 
calibrating testing-machines from time to time ; the weighing 
system is usually independent of the system for applying 
power, although in certain early machines a single lever 
mounted on a fulcrum was used, as shown in Figs. 29 and 30, 
and in which the power system and weighing system were com- 
bined, the power applied being measured by multiplying the 
weight by the ratio of the lever-arms b/a. 



§ 6 1.] STRENGTH OF MA TE RIALS— TESTING-MACHINES. 



The power system, when independent of the weighing sys- 
tem, usually consists of a hydraulic press, as shown in Fig. 31, or 
a train of gears, as shown in Fig. 32. The principal advantage 
of having the power system independent from the weighing 
system is due to the fact that under such conditions the 
stretching of the specimen, which almost invariably takes place, 
does not affect the accuracy of weighing. 

The shackles or clamps for holding the specimen vary with 
the strain to be applied. The clamps for tension-tests usually 
consist of truncated wedges which are inserted in rectangular 





Fig. 31. — Hydraulic Press. 



Fig. 32.— Form of Gearing. 



openings in the heads of the testing-machines, and between 
which the specimen is placed. The interior face of the wedges 
is for flat specimens, plane or slightly convex and serrated, but 
for round or square specimens is provided with a triangle or 
V-shaped groove into which the head of the specimen is placed. 
When the strain is applied to the specimen the wedges are 
drawn close together, exerting a pressure on the specimen 
somewhat in proportion to the strain and often injurious to its 
strength. In many instances shackles with internal cut threads 
are used, into which specimens provided with a corresponding 
external thread are screwed ; this latter construction is much 
preferable to the former, though adding much to the expense 
of preparing the specimen. It is very important that the 
shackles should hold the specimens nrmly and accurately in 



90 



EXPERIMENTAL ENGINEERING. 



[§6i. 



the axis of the machine and should not exert a crushing strain 
which is injurious to the material. 

General Character of Testing-machines. 

Testing-machines are classified as vertical or horizontal, 
depending upon the position of the specimen ; this, however 
is not an important structural difference, although certain 
classes of machines are better adapted for the one method of 
testing than the other. Machines may also be classified as 
tensive, compressive, or transverse machines, depending upon 
whether they are better suited to apply one class of stresses than 
the other, but as the method of testing is generally dependent 
simply upon the method of supporting the specimen, this 
classification is of little importance structurally. Machines can 




Fig. 33.— Wicksteed, Martens, Michaelis, Buckton. 

perhaps be best classified by the form and character of weigh- 
ing mechanism, it being generally understood that power may 
be applied through the medium of gears or by a hydraulic 
press, as desired, and with any class of machine. 

Under this classification we have: 

First, the simple lever machines, forms of which have been 
shown in Figs. 29 and 30, in which the power for breaking 
was obtained from the weighing mechanism. Fig. 33 shows 
a single-lever machine much used at the present time in Eng- 
land, in which the power is applied to the specimen at B, and 
the amount of stress is determined by the position of the jockey 
weight w, and the amount of weight on the poise R. 






§ 6 1 .] S TRENG TH OF MA TERIA L S— TES TING -MA CHINES. 9 1 



*§> 




A single-lever machine in which the lever is of the second 
order is shown in Fig. 34. The specimen is placed between 
the fulcrum and the weigh- 
ing mechanism. The latter 
consists of a hydraulic cy- 
linder with diaphragm and 
attached gauge, and is in- 
teresting as being the proto- 
type of the Emery testing- 
machine. 

Second, differential-lever machines, one kind of which is 
shown in Fig. 35 . This consists of a single lever with poise, to 
which the draw-head is connected by links placed at unequal 



Fig. 34.— Thomasset. 




Fig. 35.— Riehle:. 

distances from the fulcrum. A machine of this form was 
manufactured at one time by Riehle Brothers.* 

Third, compound-lever machines. These have been much 
used in America for the last twenty years, and are manufactured 
by Riehle Brothers, Olsen, and Fairbanks. In these machines 
power is usually applied by gearing; at least, such a construc- 
tion is generally preferred in this country. The diagram, 

* The forces acting in this machine can be represented by the following 
equation: 



Rd -f- we — 



f + S 



(af-bg). 



9 2 



EXPERIMENTAL ENGINEERING. 



[§6i. 



Fig. 36, shows the arrangement of levers adopted in the Fair- 
banks machine. Power is applied at F, specimen is placed at s 9 
and the stress is transmitted by the various levers P, E t and c 




^0=, 



ff//////J\$22^ 



Fig. 36. — Fairbanks Machine. 

to the weighing-scale. The various fulcrums marked r rest 
on a fixed support. 

Fig. 37 shows arrangement of levers adopted in the 
Olsen and Riehle machines, power being applied to the lower 
draw-head B, and the stress 
transmitted through the speci- 
men by means of the various 
levers to the weighing-scale w. 
In this diagram P denotes the 
position of fixed fulcrums. By 
placing the specimen between 
the lower draw-head B and the 
platform EE, it may be broken 
by compression 



B 



C, iftE=3 



TTTti 



=CF 



1 



'I 



A IUp 



1TF 

Fig. 37. — Olskn and RiehlIs. 

By providing suitable support resting on 
the platform EE a transverse stress can be applied. 

Fourth, direct-acting hydraulic machines. Fig. 38 shows 
a simple form of a hydraulic machine, in which power is 
applied by liquid pressure to move the piston R, the speci- 
men being located at s for tension and at a'b f for compression. 
Machines of this kind have been built of the very largest 
capacity, as for instance that designed by Kellogg at Athens, 
Pa., has a capacity of 1,250,000 pounds, and at the Phoenix 



§ 6 1 . ] S TRENG TH OF MA TERIA LS— TES TING-MA CHINES. 9 3 

Iron Works has a capacity of 2, 000,000 pounds, while one 
built by Professor Johnson at St. Louis has a capacity of 
about 750,000 pounds. In all these machines the stress is 
measured by multiplying the readings of the gauge by a con- 
stant depending upon the area of the cylinder, the effect of 




E D 

— r -» • 

Fig. 38. — Kellogg, Johnson. 

friction being eliminated by keeping the piston rotating, or in 
other cases neglecting it or determining its amount and cor- 
recting the results accordingly. Such machines are not 
adapted for accurate testing, but are suited for testing of a 
character which permits considerable variation from the 
correct results. 

A modified form of the simple hydraulic machine was 
made by Werder in 1852, having a capacity of 100 tons, the 
principle of its construction being shown in Fig. 39. In this 
machine the line of action of the stress is in RF, while that 




Fig. 39.— The Werder, 1852. 

of the resistance is in the line Ad which is to one side of RF, 
These forces are balanced by adjusting the weights on the 
scale-beam, thus providing means of weighing the force 
applied to the specimen. 

Fig. 40 is a sketch of the working parts of the Maillard 
machine, in which the weighing apparatus consists of a fluid 
which is put under pressure by means of a diaphragm against 



94 



EXPERIMEN TA L ENGINEERING. 



[§ 61. 



which the stress applied to the specimen reacts. This force 
is measured on a hydraulic gauge similar in many respects 
to the weighing apparatus of the Emery testing-machine. 




Fig. 40. — Maillard. 



Fifth, the Emery machine. The general principle of the 
Emery testing-machine is shown in Fig. 41. Fewer is 
applied by means of the double-acting hydraulic press R so as 
to break the specimen either in tension or compression, as 
desired. The specimen is placed at s, and the stress trans- 
mitted is received, if in tension, first by the draw-head BB, 
thence transmitted to the draw-head B' B\ thence in turn to 




Fig. 41. — Emery. 

the fluid in the hydraulic support v through a frictionless dia- 
phragm, from which the fluid pressure is transmitted to the 
vessel with the smaller diaphragm d, the pressure of which is 
balanced and weighed on the weighing-scale w. If the 
specimen is in compression the force is transmitted by the 
draw-head BB to the bottom of the hydraulic support v, thus 
crowding the hydraulic support and its contents against the 
diaphragm, which in turn causes a liquid pressure which is 
measured on the weighing-scale as before. The springs which 



§ 6 1 . ] S TRENG TH OF MA TEE I A LS-TES TING- MA CHINES. 9 $ 

receive the pressure of the liquid are adjusted by screws rr, 
connected to the frame, and of sufficient strength to resist the 
greatest stress applied in compression. 

In order that the levers of a testing-machine may transmit 
the force to the weighing poise with as little loss as possible, 
and in such a manner that a large force can be balanced by a 
small weight, a knife-edge bearing is in nearly every case pro- 
vided for each lever. The knife-edge as usually constructed 
is a piece of hardened steel with a sharp edge which is inserted 
rigidly in the weighing-lever and rests upon a hardened steel 
plate fastened to the fulcrum, although in some cases the 
positions of knife-edge and plate are reversed. The knife-edge 
should be as sharp as it can be made without crumbling or cut- 
ting the contact-plate, and it should be kept clean and free 
from dirt or rust in order to keep the friction at the lowest 
possible point. In practice the knife-edge is made from 30 
to 1 10 degrees, depending upon the load. Machines of the 
type shown in Fig. 37 have been constructed in which the 
friction and other losses as shown by trial did not exceed 100 
pounds in 100,000. 

The fulcrums for supporting the levers in the Emery test- 
ing-machine are thin plates of steel rigidly connected to both 
the lever and its support, as shown in Figs. 41, 51, and 52. 
A flexure of the fulcrum-plates is produced by an angular 
motion of the levers ; but as this motion in practice is small,, 
and as the fulcrums are very thin, the loss of force is inappre- 
ciable and all friction is eliminated. The plate fulcrums also 
possess the advantage of holding the levers so that end motion 
is impossible, and thus preventing any error in weighing due 
to change of lever-arm. The peculiar form of the plate ful- 
crums is such as to be unaffected by dirt ; furthermore in 
practice a higher degree of accuracy in weighing has been ob- 
tained than is possible with knife-edge levers. The principal 
characteristics of the Emery machine are, first, the hydraulic 
supports, which are vessels filled with a liquid and having a 
flexible side or diaphragm, which transmits the pressure to a 
similar support in contact with the weighing apparatus. The 



9 6 



EXPERIMENTAL ENGINEERING. 



[§62. 



detailed construction of an hydraulic support as used in a ver- 
tical machine is shown in Fig. 50, its method of operation in 
Fig. 41. Second, the peculiar steel-plate fulcrums, which 
have been described. These together with excellent work- 
manship throughout have served to make the Emery testing- 
machine an instrument of precision with a greater range of 
capacity and an accuracy far superior to that of any other 
machine. 

Fig. 42 gives a perspective view of the Emery machine 
with the working parts marked the same as in the diagram. 




Emery Horizontal Machine. 



In this figure M is the pump for operating the hydrjulic 
press, hh' the connecting piping, TT screws forming a part 
of the frame and used for adjusting the position of the press 
for different lengths of specimens, c<nd of sufficient strength to 
withstand the shock due to breaking; Pis the weighing-case, 
which contains a very elaborate system of weights which can 
be applied without handling, as described in detail later. 

62. Weighing System. — The weighing system in the pres- 
ent English machines, and in former ones built in this country, 
consists of a single lever or scale-beam, along which can be 



§63.] STRENGTH OF MATERIALS— TESTING-MACHINES. 97 

moved a poise, and which can be connected by one or more 
levers to the test specimen. Such machines are objectionable 
principally from the space occupied. 

The weighing device in nearly all recent machines consists 
of a series of levers, arranged very much as in platform-scales, 
finally ending in a graduated scale-beam over which a poise is 
made to move. The machines are usually so constructed that 
the effect of the strain on the specimen is transmitted into 
a downward force acting on the platform, and the effect of 
a given stress is just the same as a given load on the plat- 
form. 

The weighing-levers usually consist of cast-iron beams car- 
rying hardened steel knife-edges, which in turn rest on har- 
dened-steel bearing plates. This is the system adopted by most 
scale-makers for their best scales. 

In the Emery testing-machines, which are especially noted 
for their accuracy and sensitiveness, the knife-edges and bear- 
ing plates are replaced by thin plates of steel, the flexibility of 
which permits the necessary motion of the levers. 

The weighing device should be accurate, and sufficiently sen- 
sitive to detect any essential variation in the stress. The 
amount of sensitiveness required must depend largely on the 
purposes of the test. An amount less than one tenth of one 
per cent will rarely make any appreciable difference in the re- 
sult, and probably may be taken as the minimum sensitiveness 
needed for ordinary testing. Means should be provided for 
calibrating the weighing device. This can be done, in the class 
of machines under consideration, by loading the lower platform 
with standard weights and noting the corresponding readings 
of the scale-beams. Testing-machines may be calibrated with a 
limited number of standard weights, by the use of a test- 
specimen, which is not to be strained beyond the elastic limit. 
The weights are successively added and removed, and strain is 
maintained on the test-piece, equal to the reading on the cali- 
brated portion of the scale-beam. 

63. The Frame.— The frame of the machine must be 
sufficiently heavy and strong to withstand the shock produced 



9$ EXPERIMENTAL ENGINEERING, [§ 65. 

by a weight equal to the capacity of the machine suddenly ap. 

plied. 

The weighing levers must sustain all the stress or force act- 
ing on the specimen, without sufficient deflection to affect 
accuracy of the weighing, and the frame must be able to sus- 
tain the shock consequent upon the sudden removal of the 
load, due to breaking, without permanent set or deflection. 

64. Power System. — The power to strain or rupture the 
specimen is usually applied through the medium of a train of 
gears or by a hydraulic press, operated by power or hand. 
The hydraulic machine is very convenient when the stress is 
less than 50,000 pounds; but if there is any leakage in the 
valves, the stress will be partially relieved the instant the pump 
ceases to operate, and difficulty may be experienced in ascer- 
taining the stretch for a given load. 

65. Shackles. — The shackles or clamps for holding the 
specimen vary with the strain to b^ applied. These clamps for 
tension tests usually consist of truncated wedges which are in- 
serted in rectangular openings in the heads of the testing-ma- 
chines, and between which the specimen is placed. The inte- 
rior face of the wedges is for flat specimens plane and serrated, 
but for round or square specimens it is provided with a trian- 
gular or V-shaped groove, into which the head of the specimen 
is placed. When the strain is applied to the specimen these 
wedges are drawn closer together, exerting a pressure on the 
specimen somewhat in proportion to the strain and often in- 
jurious to its strength. In tensile testing it is essential to the 
correct determination of the strength of the specimen that the 
force shall be applied axially to the material ; in other words, it 
shall have no oblique or transverse component. This requires 
that the wedge clamps shall be parallel to the specimen, and 
that the heads which contain the clamp shall separate in a 
right line and parallel to the specimen. 

This construction is well shown in the following description 
of the clamps used in the Olsen and Riehle testing-machines. 

A plan and section of the draw-heads used with the Olsen 
machine is shown in Fig. 43. The small numbers refer to 



§ 65.] STRENGTH OF MA TERIALS— TESTING-MACHINES. 99 

the same part in each view, and also in Figs. 56 to 60, so that 
any part can be easily identified ; 60, 59 is a counterbalanced 
lever used to prevent the wedges falling out when the strain 
is relieved ; 63, 63, is a screw connected to a plunger for ad- 
justing the space into which the wedge-clamps are drawn. A 
lateral motion of the specimen is obtained by unscrewing on 
one side and screwing up simultaneously on the other side : 




Fig. 43. — Draw-head to Olsen's Testing-machine. 

this adjustment is of advantage in some instances in centring 
the specimen. For use of the other parts shown in Fig. 43, 
see Art. 64. 

The clamps used by Riehle Brothers for holding flat speci- 
mens are shown in Fig. 44 and Fig. 46, as follows : 

LOFCX 



100 



EXPERIMENTAL ENGINEERING. 



[§6o. 



Fig. 45 is a plan of wedge-clamp, with specimen in posi- 
tion ; CC, curve-faced wedges; D, specimen; A, draw-head; 
and BB tension-rods. 






Fig. 44- 



Fig. 45. 



Fig. 46. 



Fig. 46 is a sectional view of same. Fig. 44 5s a view of 
the wedge-faced clamp. The inclination of the surfaces of the 
wedges are exaggerated in the drawings,so as to distinctly set 
forth their features. 

Wedges have been made with spherical backs, and a por- 
tion of the draw-heads mounted on ball surfaces in order to 
insure axial strains. Special holders into which screw-threads 
have been cut have been used with success, and in many- 
instances the specimens have been fastened to the draw-head?, 
by right and left threaded screws. 

66. Specifications for Government Testing-machine.— 
The large machine in use by the. United States Government at 
the Watertown Arsenal was built by Albert H. Emery. The 
machine is not only of large capacity, but is extremely delicate 
and very accurate. A perspective view of the machine is 
shown in Fig. 28. 

The requirements of the United States Government as ex- 
pressed in the specifications, which were all successfully met f 
were as follows : 



§ 66.] STRENGTH OF MATERIALS— TESTING-MACHINES. IOI 

n n& 




102 EXPERIMENTAL ENGINEERING. [§ 6/, 

1st. A machine with a capacity in tension or compression 
of 800,000 pounds, with a delicacy sufficient to accurately reg- 
ister the stress required to break a single horse-hair. 

2d. The machine should have the capacity of seizing and 
giving the necessary strains, from the minutest to the greatest, 
without a large number of special appliances, and without 
special adjustments for the different sizes. 

3d. The machine should be able to give the stresses and 
receive the shocks of recoil produced by rupture of the speci- 
men without injury. The recoil from the breaking of a speci- 
men which strains the machine to full capacity may amount 
to 800,000 pounds, instantly applied. The machine must bear 
this load in such a manner as to be sensitive to a load of a 
single pound placed upon it, without readjustment, the next 
moment. 

4th. The parts of the machine to be at all times accessible. 

5th. The machine to be operated without excessive cost. 

67. Description of Emery Testing-machine. — These ma- 
chines are now constructed by Wm. Sellers & Co. of Phila- 
delphia, under a license from the Yale & Towne Mfg. Co. of 
Stamford, Conn. 

The following description will serve to explain the principle 
on which the machine acts : 

The machine consists of the usual parts: 1. Apparatus 
to apply the power. 2. Clamps for holding the specimen. 
3. The weighing device or scale. 

1. The apparatus for applying power consists of a large hy- 
draulic press, which is mounted on wheels as shown in the en* 
gravings, Fig. 28 and Fig. 47, and can be moved a greater or 
less distance from the fixed head of the machine. Two large 
screws serve to fix or hold this hydraulic press in any position 
desired, according to the length of the specimen : and when 
rupture is produced the shock is received at each end of these 
screws, which tend to alternately elongate and compress, and 
take all the strain from the foundation. 

2. Clamps for holding the specimen. These are peculiar to 
the Emery machine, and are shown in Fig. 47 in section. This 



§ 6?.] STRENGTH OF MA TE RIALS— TESTING-MA CHINES. 1 03 

figure also shows a section of the fixed head of the machine, 
and a portion of the straining-press, with elevation of the 
holder for the other end of the specimen. 

The clamps, numbered 1484 in Fig. 47, are inserted between 
two movable jaws (1477), which are pressed together by a 




Fk 



18. — Elevation of the Vertical Machine. 



Fig. 49. — Scale-beam and Case. 



hydraulic press (1480), resting on the fixed support (1476). By 
this heavy lateral pressure force equal to 1,000,000 pounds can 
be applied to hold the specimen. The amount of this force is 
shown by gauges connected to the press cylinder, and can be 
regulated as required. 



104 EXPERIMENTAL ENGINEERING. [§ 76. 

For the vertical machines these shackles or holders are ar- 




Fig. 50.— The Base-frame and Abutments. 

ranged so as to have sufficient lateral motion to keep in the 
line of the test-piece. 

3. The weighing device. This is the especial peculiarity of 



§ 6y.] STRENGTH OF MATERIALS— TESTING-MACHINES. 105 

the Emery machine: instead of knife-edges, thin plates of 
steel are used, which are flexed sufficiently to allow the neces- 
sary motion of the levers. The steel used varies from 0.004 to 




Fig. 51. — Beam for Platform-scale. 



0.05 inch thick, and the blades are so wide that the stress 
does not exceed 40,000 to 60,000 pounds per square inch. 

Fig. 52 shows the form of fulcrums used for light forces 
when the steel fulcrums are in tension. 




Fig. 52. — Clamping Suspension Fulcrums. 



The method of measuring the load is practically that of 
the hydraulic press reversed, but instead of pistons, diaphragms 
having very little motion are used. Below the diaphragm is 
a very shallow chamber connected by a tube to a seconr 



106 EXPERIMENTAL ENGINEERING. [§ 6 J. 

chamber covered with a similar diaphragm, but of a different 
diameter. Any downward pressure on the first diaphragm is 
transmitted to the second, giving a motion inversely as the 
squares of the diameters. This latter motion may be farther 
increased in the same manner, with a corresponding reduction 
in pressure, or it may at once be received by the system of 
weighing levers. The total range of motion given the first 
diaphragm in the 50-ton testing-machine is ^oWo P art of an 
inch, but the indicating arm of the scales has a motion of T -i~g 
of an inch for each pound. This increase of motion and cor- 
responding reduction of pressure is accomplished practically 
without friction. These parts will be well understood by Figs. 
50, 51, and 52. The diaphram with connecting pipe,/, is 
shown between the abutments EE in Fig. 50. 

Fig. 48 shows the elevation of the vertical machine arranged 
for transverse tests. Fig. 49 shows the scale-beam and case, and 
Fig. 50 is a section of the base-frame and hydraulic supports. 
In this last figure the diaphragm, filled with liquid, is placed 
between the frames EE. These frames are allowed the neces 
sary but slight vertical motion by the thin fulcrum-strips b and 
c, but at the same time are held from lateral motion. The 
frame EE and diaphragms are supported by springs d, so as 
to have an initial tension acting on the test-piece. The dia- 
phragm and its enclosing rings fill the whole space between 
the frame to within 0.005 inch, which is the maximum amount 
of motion permitted. 

The pressure on the diaphragm between the frames EE is 
communicated by the tube /to a similar diaphragm in com- 
munication with the weighing-levers. Fig. 5 1 represents the 
weighing-levers for platform-scales. In case a diaphragm is used 
it is placed beneath the column A ; the motion of the column 
A is communicated to the scale-beams by a system of levers 
as shown. 

The scale-beam of the testing-machine is shown in Fig. 49, 
and is so arranged that by operating the handles on the out- 
side of the case the weights required to balance the load can 
be added or removed at pleasure- The device for adding the 



§68.] STRENGTH OF MATERIALS— TESTING-MACHINES. I07 



weights is shown in Fig. S3- a, b, r, d, e, and /are the weights, 
which are usually gold-plated to prevent rusting. These when 
not in use are carried on the supports A and B by means of 
pins. When needed, these supports can be lowered by the out- 
side levers, and as many weights as are 
needed are added to the weighing-poise 
CD. 

68. Riehle Brothers' Hydraulic 
Testing-machines. — The testing-ma- 
chines built by Riehle Brothers of Phil- 
adelphia vary greatly in principles and 
methods of construction. In the ma- 
chines built by this firm, power is ap- 
plied either by hydraulic pressure or by 
gearing, and the weighing device con- 
sists of one or more levers working .over 
steel knife-edges, as in the usual scale 
construction. 

Machines have been built by this firm 
since 1876. The form of the first 
machine constructed was essentially 
that of a long weighing-beam sus- 
pended in a frame and connected by 
differential levers to the specimen, the 
power being applied by a hydraulic 
press. The later forms are more com- 
pact. The standard hydraulic machine 
as constructed by this firm is shown 
in Fig. 54. In this machine the cylin- 
der of the hydraulic press, which is 
situated directly beneath the specimen, 
is movable, and the piston is fixed. 

This motion is transmitted through the specimen, and is 
resisted by the weighing levers at the top of the machine, 
which are connected by rods and levers to the scale-frame. 
Two platforms connected by a frame are carried by the weigh- 
ing levers : the upper one is slotted to receive the wedges for 




Fig. S3*— Device for Adding 
or Removing Weights. 



io8 



EXPERIMENTAL ENGINEERING. 



BC9. 



holding the specimen : the lower one forms a plane table. The 
intermediate platform, or draw-head, can be adjusted in dif- 
ferent positions by turning the nuts on the screws shown in 
the cut. For tension-strains the specimen is placed between 
the upper and intermediate head; for compression it is placed 
between the intermediate and lower heads. An attachment is 
often added to the lower platform, so that transverse strains 
can be applied. 

The cylinder is connected by two screwed rods to the 
intermediate platform or draw-head, and when it is forced 




Fig. 54. — Hydraulic Testing-machine. 

downward by the operation of the pump this draw-head if 
moved in the same direction and at the same rate. 

69. Riehle Power Machines. — The machines in which 
power is applied by gearing are now more generally used than 
hydraulic machines. Fig, 55 shows the design of geared ma- 
chine now built by Riehle Bros., in sizes of 50,000, 100,000, and 
200,000 pounds capacity. In this machine both the gearing 
for applying the power and the levers connected with the 
weighing apparatus are near the floor and below the specimen, 
thus giving the machine great stability. The heads for hold- 
ing the specimen are arranged as in the hydraulic machine, and 
power is applied to move the intermediate platform up or down 



§69.] STRENGTH OF MATERIALS— TESTING-MACHINES. io 9 



as required. The upper head and lower platform form a part 
of the weighing system. The intermediate or draw-head may 
be moved either by friction-wheels or spur-gears at various 




speeds, which are regulated by two levers convenient to the 
operator standing near the scale-beam. 

The poise can be moved backward or forward on the scale* 



I IO 



EXPERIMENTAL ENGINEERING. 



[§70- 



beam, without disturbing the balance, by means of a hand- 
wheel, opposite the fulcrum on which the scale-beam rests. 

The scale-beam can be read to minute divisions by a 
~* r ernier on the poise. 

70. Olsen Testing-machine. — General Fornu — The ma* 




Fig. 56.— The Olsen Testing Machine. Front View. 

chines of Tinius Olsen & Co. of Philadelphia are all operated 
toy' gearing, driven by hand in the machines of small capacity, 
aiid by power in those of larger capacity. 

The general form of the machine is shown in Figs. 56 and 
57, :rom which it is seen that the principles of construction 
t^v, the same as in the machine last described. 



§ 7 l • J S TR !-NG TH OF MA TERIA L S— TESTING-MA CHINES. I I I 

The intermediate platform or draw-head is operated by- 
four screws instead of by two, and there is a marked difference 
in the arrangement of the weighing-levers and in the gearing. 

The machine can be operated at various rates of speed in 
either direction, and is readily controlled by convenient levers. 




71. The Olsen Autographic Apparatus. — This apparatus 
for drawing strain-diagrams is entirely automatic, and is 
Operated substantially as follows : 

The diagram is drawn on a drum (103), parallel to the scale- 
beam, by a pencil actuated by a screw-thread cut to a fine pitch 



112 



EXPERIMEN TAL ENGINEERING. 



[§7L 



on the end of the rod which actuates the poise (106), so that 
the pencil will move in a definite ratio to that of the poise. 
The drum is actuated by the stretch of the specimen. This 
is brought about by four fingers shown in Fig. 56, and on a 
larger scale in Fig. 58 by numbers 82 and 83. These fingers, 
shown in plan in Fig. 59, tend to separate and follow any 
motion of the collars (65) placed on the test-piece, as shown in 
Fig. 56; the motion of these fingers is multiplied five times, 




• [] llJL_J'lLj 



Fig. 58. 

and connected by steel bands to the drum, 102, in such a man* 
ner that the resultant force only is effective to rotate the drum. 
The poise is moved by a friction device attached to the 
main power system, which is thrown into or out of gear auto- 
matically by an electric current, as required to keep the beam 
floating ; the current passes through the scale-beam in opposite 
directions, according as the place of contact is above or below 






§ 7 2 -] STRENGTH OF MA TERIA IS— TESTING-MACHINES. I I 3 

the beam. Finally, an alarm-bell is rung whenever the scale- 
poise moves beyond its normal distance, thus calling the at- 
tention of the operator. 

Gauge-marking Device. — A special and very ingenious ar- 
rangement, shown in Fig. 60, is used to hold the test-piece and 
mark the extreme gauge-marks in any position desired. 

72. Parts of Olsen Machine. — The following reference 
numbers to the parts of the Olsen machine will serve to show 
the construction : 



I. Entablature. 


61. Plungers for slides 51. 


2. Columns. 


62. Screws for 61. 


3. Platform supporting columns. 


63. Screw-bolt. 


4. Pivots. 


64. Collars or clamps for caliper bear- 


5. Lower moving head. 


ing. 


22. Sleeve on driving-shaft. 


72. Guiding-block. 


24. Rock-shaft operating lever shifting 73. Cam. 


22. 


74. Lever moving 87. 


25. Hand-lever operating 24. 


75. Sliding-blocks. 


26, 27. Pulleys rotating driving-shaft. 


78. Polygonal prism in 75. 


28, 29. Friction-clutches engaging 26 82, 83. Calipers. 


with driving-shaft. 


85. Arm of caliper. 


30. Sleeve operating clutches. 


86. Clamps. 


31. Forked lever controlling sleeve 30. 95. Cord operating recording-cylinder. 


33. Hand-lever ope;ating 30. 


96. Pulley. 


34. Grooved wheel on driving-shaft. 


97. Lever. 


40. Tilting bearing. 


98. Fulcrum to 97. 


41. Band-wheel. 


99. Pulley or sheave. 


42. Endless band. 


100. Drum or winding-barrel of 102. 


44. Helical spring. 


101. Link. 


46. Fulcrum of lever 117. 


102. Recording-cylinder. 


48. Specimen under test. 


103. Pencil. 


49. Gripping jaws. 


104. Screw. 


50. Projecting flanges on jaws 49. 


105. Screws shifting 106. 


51. Block-slide. 


106. Poise or weight. 


52. Grooves in 51. 


in. Balancing pivot of beam. 


53. Slotted slide supporting 49. 


117. Force multiplying lever. 


54. Opening in 53. 


118. Weighing-beam. 


55. Eye in 53. 


118'. Slide to small poise on 118. 


56. Bolt connecting 53 and 57. 


119. Link. 


57. Lever to open and shut jaws. 


144. Endless band for moving poise. 


58. Fulcrum of 57. 


145. Guiding-pulleys. 


59. Counterweight. 


146. Grooved wheel. 


60. Handle of lever 57. 





14 



EXPERIMENTAL ENGINEERING. 



[§73« 



73. Thurston's Torsion Testing-machine. — Both the 
breaking-strength and the modulus of rigidity can be obtained 
from the autographic testing-machine invented by Professor 
Thurston in 1872. 




Fig. 61.— Thurston^ Autographic Torsion Testing-machine. 



In this machine the power is applied by a crank at one 
side, tending to rotate the specimen, the specimen being con- 
nected at the opposite end to a pendulum with a heavy 
weight. 

The resistance offered by the pendulum is the measure of 



§ 73-] STRENGTH OF MA TERIALS— TESTING-MACHINES. I I 5 



the force applied, since it is equal to the length of the lever- 
arm into the sine of the angle of inclination, multiplied by the 
constant weight P. A pencil is carried in the axis of the 
pendulum produced, and at the same time is moved parallel to 
the axis of the test-piece by a guide curved in proportion to 
the sine of the angle of deviation of the pendulum, so that the 
pencil moves in the direction of the axis of the specimen an 
amount proportional to the sine of this angle. A drum carry- 
ing a sheet of paper is moved at the same rate as- the end of 
the specimen to which the power is applied. Now if the pencil 
be made to trace a line, it will move a distance around the 
drum which is equal to the angle of torsion (a) expressed in 
degrees or n measure, and it will move a distance parallel to 
the axis of the test-piece proportional to the moment of ex- 
ternal forces, Pa. 

The diagram Fig. 62, from Church's " Mechanics of En- 
gineering," shows the working portions of the machine very 
clearly. In the figure P is the pendulum, the upper end of 




Fig. 62. 



which moves past the guide WR, and is connected by the link 
FA with the pencil A T. The diagram is drawn on a sheet of 
paper on the drum, which is rotated by the lever b. The 



Il6 EXPERIMENTAL ENGINEERING. \%7\ 

drum moves through the angle a, relatively to the pendulum 
which "moves through the angle fi. The test-piece is inserted 
between the pendulum and drum. 

The value of a in degrees can be found by dividing the 
distance on the diagram by the length of one degree on the 
surface of the paper on the drum, which may be found by 
measurement and calculation. 

Application of the Equations to the Strain-diagram. — For 
the breaking-load apply equation (23) of Chapter III., 

Pa=pJ p -±e (23) 

The external moment Pa equals Pr sin /?, in which P is 
the fixed weight, r the length of the pendulum, fi the angle 
made with the vertical. Hence 

Pr sin fi = pj p -$- e. 

In this equation P and r are constant, and depend upon the 
machine ; I P and e are constant, and depend upon the test- 
piece. 

sin fi is the ordinate in inches to the autographic strain- 
diagram, and can be measured ; knowing the constant, p s may 
be computed. 

p s = Pr sin fie -f- I p . 

For the modulus of rigidity, apply equation (22^), Chapter 
III., page 72. 

E s =p s l -5- ea = Plr sin fi -4- I p tx. 

In this equation sin fi is the ordinate to the strain-diagram, and 
a the corresponding abscissa, the other quantities are constant, 
and depend on the machine or on the test-piece. 

The Resilience (see equation (25), page 83) is the area of the 
diagram within the elastic limit, expressed in absolute units. 

U = iPaa = \Pr sin fia a 



§75-] STRENGTH OF MATERIALS— TESTING-MACHINES. II? 

The Helix Angle (see equation (22), page 82) d = ea -±- 1, in 
which / is the length of the specimen in inches. The elongation 
of the outer fibre can be computed by multiplying / by secant 6. 
The per cent of elongation is equal to secant tf. (Sec 6 is 
equal to the square root of 1 -f- tan 2 d.) 

74. Machine Constants. — To obtain the Constants of the 
Machine, — First, the external moment Pa. This is obtained on 
the principle that it is equal to any other external moment 
which holds it in equilibrium. Swing the pendulum until its 
centre-line is horizontal ; support it in this position by a strut 
resting on a pair of scales; the product of the corrected reading 
of the scales into the distance to the axis on the arm will give 
Pa, Check this result by trials with the strut at different points. 
Correct for friction of journal. Second, the value of the scale of 
ordinates can be obtained by measuring the ordinate for j3 = 90 
and for fi = 30 , since sine 90 = 1 and sine 30 = -|. Third, the 
value of the scale of abscissae can be obtained by dividing the 
abscissa on the diagram by the radius of the drum including 
the paper. This may be expressed in degrees by dividing by 
the length of one degree. 

Constants of the Material are obtained by measuring the 
dimensions of the specimen. The values of /and e are given 
on page 78. 

Conditions of Accuracy. — In obtaining these values, the fol 
lowing conditions are assumed : Firstly, the test-piece is exactly 
in the centre of motion of the pendulum and of the drum ; sec- 
ondly, the pencil is in line of the pendulum produced ; thirdly, 
the curve of the guides is that of the sine of the angle of devia- 
tion ; and, fourthly, the specimen is held firmly from rotation 
by the shackles or wedges, and yet allowed longitudinal motion. 
These constitute the adjustments of the machine, and must 
be carefully examined before each test. Any eccentricity of 
the axis of the specimen will lead to serious error. 

6$. Power Torsion-machine. — This machine is shown in 
Fig. 63a. Power is applied at various rates of speed by means 
of the gearing shown. The specimen is held by means of two 
chucks: the one on the left is rotated an amount shown by the 



n8 



EXPERIMENTAL ENGINEERING, 



[§75* 



graduated scale in degrees ; the one on the right is prevented 
from rotating by a lever, so connected to the scale-beam that 
when it is balanced the reading is proportional to the torsional 
force or external moment transmitted through the specimen, 
expressed in foot-pounds, inch-pounds, or any other units 
desired. The weighing head is suspended so as to permit free 
elongation of the specimen. The chucks used have self-cen- 
tering jaws which will hold the specimen rigidly and central 
during application of the stress. 

Machines of the general class shown in the figure are made 
in Philadelphia both by Riehle Brothers and Tinius Olsen, 




Pig. 63.— The Riehle Torsion Machine. 



which are adapted to testing of specimens of varying diameters 
and lengths. In the Riehle machine shown, the adjustment 
for specimens of various lengths is made by moving the power 
head ; in the Olsen machine the adjustment is made by mov- 
ing the weighing head and scale-beam, which are arranged in 
a plane at right angles to the specimen. 

The graduated scale attached to the machine for angle of 
torsion should seldom be used for that purpose, as the specimen 
is quite certain to slip to greater or less extent in the machine 
and considerable error will result. 



§7$.]STJ?EJVGr// OF MATERIALS— TESTING-MACHINES. IlSa 

In the Olsen machine the angle of torsion may be measured 
by clamping dogs on the specimen at each end so as to engage 
the projections, shown at b, Fig. 63a, of the index-rings, which 
are free to move over the graduated scales of the chucks. The 
angle of torsion of the specimen, for a length represented by the 
distance between the centres of the dogs, is the angle turned 
through by the movable chuck less the sum of the angles through 




Fig. 63c. — Olsen Torsion Machine. 



which the index- rings are pushed by the dogs. Let a\= angle 
through which movable chuck is rotated, a^ = angle through 
which index-ring on the movable chuck is pushed by the dog, 
as = angle through which index- ring on fixed chuck is pushed by 
the dog, and a = angle of torsion. Then 
a=ai — (« 2 4-a 3 ). 

This angle is measured through short ranges by means of two 
index-arms clamped to the specimen, as shown at c. One arm 
carries a pointer which plays over an arc (d), graduated in inches, 
whose centre of curvature is the centre of the specimen. The 
distance traversed by the pointer divided by the radius of the arc 
gives the angle of torsion in circular measure. 

The constant of the machine, or the value of the graduations 



n8£ 



EXPERIMEN TA L ENGINEERING. 



[§ 75- 




on the scale-beam, may be found as follows (see Fig. 636) : The 
fixed chuck is rigidly connected to link K as shown. The tor- 
sion moment (Pa) on the specimen tends to rotate the chuck and 

link as indicated by the arrow. The 
only additional forces acting on K are 
the vertical forces of strut P\ and of 
the frame through the knife-edges at 
R. The right end of link K is pre- 
vented from dropping down, when no 
load is on the specimen, by a strut act- 
ing upward at R (not shown in fig- 
FlG - 6 3 & - ure). R may therefore act either 

upward or downward, depending upon the intensity of Pa. 
The weight of K may, howerer, be entirely neglected since the 
counterpoise of the machine may be so set that the system is in 
equilibrium with no stress on the specimen. 

With the dimensions shown, weight of poise =40 pounds, 
length between divisions on scale-beam = § inch, consider K 
as a free body. Then I(Pa)=o and IY=o. From which 

Pa = i2P!+8R and Pi=P, 
or Pa = 2oPi (1) 

Pi acts at a lever-arm of 2 inches in the lower lever G, and P 2 
acts at a lever-arm of 30 inches. Then 

2 P 1 =3oP 2 and Pi = i5P 2 (2) 

P acts on scale-beam at a lever-arm of 2 inches, and this moment 
must be balanced by moving the poise W along the distance x. 
From which 

2P 2 = WX. ( 3 ) 

From (1), (2), and (3) we have 

Pa = 20 X 1 5 X 20X. 
Make x = 1 scale division = § inch. 

Pa = 4000 inch-pounds. 

Since the value of each division as marked on scale-beam is 
200, the constant of the machine is 20. 



§ 77-] STRENGTH OF MATERIALS— TESTING-MACHINES. H9 

For an accurate determination of the angle of torsion, it 
is important that the specimen be kept straight during the 
application of stress, and that the angle of torsion be measured 
from arcs or scales having the same centre as the specimen. 
The method of measuring the angle of torsion, as described 
for a specimen in the Olsen machine, is accurate and generally 
applicable. 

76. Impact-testing Machine. — The Drop Test — Testing by 
Impact. — This test, see Art. 105, is recommended for material 
used in machinery, railroad construction, and generally when- 
ever the material is likely to receive shocks or blows in use. 

This test is usually performed by letting a heavy weight 
fall on to the material to be tested. The Committee on Stand- 
ard Tests of the American Society of Mechanical Engineers 
recommend that the standard machine for this purpose consist 
of a gallows or framework operating a drop of twenty feet, the 
weight to be 2000 pounds, the machine to be arranged sub- 
stantially like a pile-driver. The impact machine designed by 
Mr. Heisler consists of a pendulum with a heavy bob, which 
delivers a blow on the centre of a bar securely held on two 
knife-edge supports affixed to a heavy mass of metal. This 
machine is especially designed for comparative tests of cast- 
iron ; it is furnished with an arc graduated to read the vertical 
fall of the bob in feet, and a trip device for dropping the ram 
from any point in the arc. A paper drum can be arranged 
for automatically recording the deflection of the test-pieces. 

Let W = the weight of the bob; 

h = the distance fallen through ; 
P= centre load; 
X = deflection. 



Then 
Hence 



Wk = iPK 

P=2Wh+\. 



77. Machines for Testing Cement— Cement mortar can 

be formed into cubes, and after hardening can be tested in the 



120 



EXPERIMENTAL ENGINEERING. 



[§7/. 



usual testing-machines for compression ; but tensile tests are 
usually required, and for this purpose a delicate machine with 
special shackles is needed. In order that the tests may gixe 
correct results, it is necessary that the power be applied uni- 




Fig. 64. — Fairbanks' Cement-testing Machine. 



formly, and absolutely in the line of the axis of the specimen; 
and to make different tests comparable, the specimen, or as it 
is called, the briquette, must be always of the same shape and 
size, and made in exactly the same manner. The engraving 
(Fig. 64) shows Fairbanks Automatic Cement Tester, in which the 
power is applied by the dropping of shot into the pail F. The 
specimen is held between clamps, which are regulated at the 



§77-] S TRENG TH OF MA TERIA L S— TESTING-MA CHINE S, 121 

proper distance apart by the screw P. At the instant of rup- 
ture the scale-beam D falls, closes a valve, and stops the flow of 
shot. In Fig. 64 M is a closed mould for forming a briquette, 
S the mould opened for removing the briquette, T a briquette 
which has hardened, and £7 one which has been broken. 

Directions. — Hang the cup F on the end of the beam D, as 
shown in the illustration, See that the poise R is at the zero- 
mark, and balance the beam by turning the ball Z. 

Place the shot in the hopper B, place the specimen in the 
damps NN, and adjust the hand- wheel P so that the gradu- 




Fig. 65.— Olsen's Cement-testing Machine. 



ated beam D will rise nearly to the stop K. Open the automatic 
v^alve /so as to allow the shot to run slowly. Stand back and 
leave the machine to make the test. 

When the specimen breaks, the beam D drops and closes 
the valve /. Remove the cup with the shot in it, and hang 
the counterpoise-weight G in its place. Hang the cup F on 
the hook under the large balance-ball £ } and proceed to weigh 
the shot in the ordinary way, using the poise R on the graduated 
beam D and the weights H on the counterpoise-weight G. 
The result will show the number of pounds required to break 
the specimen. 

An automatic machine designed by Prof. A. E. Fuertes has 
been in use a long time in the cement-testing laboratory at 



122 



EXPERIMENTAL ENGINEERING. 



[§77- 



Cornell University. In this machine water is supplied flowing 
from a constant head through a small glass orifice. The fall 
of the beam consequent on the breaking of the specimen in- 
stantly stops the flow of water ; the weight of this water, mul- 
tiplied by a known constant, gives the breaking-load on the 
briquette. 

The Olsen Cement-tester is shown in Fig. 65. The power is 
applied by the hand-wheel and screw, so that it strains the 




whsssup &wf.st.phil „ 
Fig. 66. — Riehle Bros.' Cement-testing Machine. 



briquette very slowly. The poise on the scale-beam is moved 
by turning a crank so that the beam can readily be kept float- 
ing. The peculiar method of mounting the shackles or hold- 
ers to insure an axial pull is well shown in the engraving. 

The Riehle cement-tester is shown in Fig. 66. The briquette 
to be tested is placed between two shackles mounted on pivots 
so as to be free to turn in every direction. 

Power is applied to the specimen by the hand-wheel below 
the machine, and is measured by the reading on the scale-beam 
at the position of the poise. Special crushing tools, consisting 



I 77.] STRENGTH OF MATERIALS— TESTING-MACHINES. 123 

of a set of double platforms, which may be drawn together by 
application of the force, is furnished with this machine. The 
specimen to be crushed is placed between these platforms, and 
the power applied as for tension. 

Besides the machines described, various machines for special 
testing are manufactured ; these machines have a limited use, 
and do not merit special description in a work of this character. 



TESTING-MACHINE ACCESSORIES. 

78. General Requirements of Instruments for Measur- 
ing" Strains. — In the test of materials it is necessary to meas- 
ure the amount of strain or distortion of the body in order to 
compute the ductility and the modulus of elasticity. The 
ductility or percentage of ultimate deformation can often be 
obtained by measurement with ordinary scales and calipers, 
since the latter is usually a large quantity. Thus in the 
tension-test of a steel bar 8 inches long, it will increase in 
length before rupture nearly or quite 2 inches ; if in the meas- 
ure of this quantity an error equal to one fiftieth of an inch 
be made, the resulting error in ductility is only one half of 
one per cent. In the measure of deformation or strain oc- 




Fig. 67.— The Wedge Scale. 

curring within the elastic limit the case is very different, as 
the deformation is very small, and consequently a very small 
error is sufficient to make a great percentage difference in the 
result. 

The instruments that have been used for this purpose are 
called extensometers, and vary greatly in form and in principle 
of construction. The instrument is generally attached to the 
test-piece, either on one or on both sides, and the strain is ob- 
tained by direct measurement with one or two micrometer- 
screws, or by the use of levers which multiply the deformation 
so that the results can be read on an ordinary scale. As a 

124 



§ 78.] 



TES TING-MA CHINE A CCESSORIES. 



125 



rule, instruments which attach to one side of the test-piece 
will give erroneous readings if the test-piece either be initially- 
curved, or strained so as to draw its axis out of a right line, 
and this error may be large or small, as the conditions vary. 

The extensometers in use generally consist of some form 
of a multiplying-lever the free end of which moves over a 
scale which may or may not be provided with a vernier, a 
micrometer-screw which is used to measure the distance 
between fixed points attached to the specimen or the roller 
and mirror and also various forms of cathetometers. 

The Paine Extensometer, which is described later, is a very 
simple and admirable form of the lever micrometer. 

The Bauschingers Roller and Mirror Extensometer. — To 
Professor Bauschinger belongs the credit of first systematically 
taking double measurements on opposite sides of a test-bar. 



f 



C 



33? 



la 



---& g 



Fig. 68. — Bauschinger's Mirror Apparatus. 

The general principle of his apparatus is shown in the annexed 
figure. It is seen to consist of two knife-edged clips, b, b> 
which are connected to the specimen and carry two hard 
ebonite rollers, d, d, which turn on accurately centred 
spindles. The spindles are prolonged, and support mirrors, 
g, g, which rotate in the plane of the figure as the spindles 
rotate. A clip, aa, is fastened to each side of the test-piece 
at the opposite extremity, and is connected by spring-pieces, 



26 



EXPERIMEN TA L ENGINEERING. 



l%7^ 



with the rollers. The spring-pieces are slightly roughened by 
file, and turn the rollers by frictional contact, so that the least 
extension of the test-piece causes a rotation of the mirror 
through an angle. If a scale be placed at s, s f and telescopes 
at e, e, the reflection of the scale will be seen in the mirror in 
looking through the telescope, and any extension of the test- 
piece will cause a variation in the reading of the scale as seen 
in the mirror. The apparatus is equivalent to a lever 
apparatus having for a small arm the radius of the roller^, 
and for a long arm the double distance of the scale from the 
mirror. With this instrument it is evidently possible to obtain 
very accurate measurements, but on the other hand the instru- 
ment is very cumbrous and difficult to use. The mean of the 
two readings with the Bauschinger instrument is the true 
extension of the piece. 

Professor Unwin obviates the use of two mirrors and two 
telescopes by attaching clips to the 
centre of the specimen and having the 
single mirror revolve in a plane at 
right angles with the plane passing 
through the clips and the axis of the 
specimen. 

Strolimeyer s Roller Extensometer 
was designed in 1886. and is a double- 
roller extensometer similar in principle 
to Buzby's and Johnson's. The appa- 
ratus consists of a roller carrying a 
needle which is centred with respect 
to a graduated scale. The roller 
moves between side-bars extending to 
clips which are fastened to each end of the specimen. The 
tension between these side-bars can be regulated by a spring 
with a screw adjustment. The objections to this form of 
extensometer are due, first, to slipping of side-bars on the 
roller, and second, to the difficulty in making the roller per- 
fectly round. 

Regarding the various forms of extensometers, the writer 




Fig. 69. — The Strohmeyer 
Extensometer. 



§8i.] 



TESTING-MACHINE ACCESSORIES. 



12' 



would say that his experience has covered the use of nearly 
every form mentioned, and none have proved to be superior 
in accuracy to that with the double micrometer-screw, and few 
can be applied so readily. 

79. Wedge-scale. — The wedge-shaped scale, Fig. 67, which 
could be crowded between two fixed points 
on the test-piece, was one of the earliest 
devices to be used. In using the scale two 
projecting points were attached to the speci- 
men, and as these points separated, the' scale 
could be inserted farther, and the distance 
measured. 

80. The Paine Extensometer. — This 
instrument, shown in Fig. 70, operates on 
the principle of the bell-crank lever, the long 
arm moving a vernier over a scale at right 
angles to the axis of the specimen. It reads 
by the scale to thousandths of an inch, and 
by means of the vernier to one ten-thou- 
sandth of an inch. Points on the instru- 
ment are fitted to indentations in one side 
of the test-piece, and the instrument is held 
in place by spring clips. It is of historical 
importance, having been invented by Col- 
onel W. H. Paine, and used in the tests of 
material for the Brooklyn Bridge, and also 
on the cables of the Niagara Suspension 
Bridge when, a few years since, the question 
of its strength was under investigation. 

81. Buzby Hair-line Extensometer. — 
This is an extensometer in which the strain 
is utilized to rotate a small friction-roller 
connected with a graduated disk as shown in 
Fig. 71. A projecting pin placed in the 
axis of the graduated disk is held between 
two parallel bars, each of which is connected FlG - 7°. 

to the specimen. The strain is magnified an amount propor- 



128 



EXPERIMENTAL ENGINEERING. 



[§ 



tional to the ratio of diameters of the disk and pin. The 
amount of strain is read by noting the number of subdivisions 
of the disk passing the hair-line. To prevent error of parallax 
in reading, a small mirror is placed back of the graduations, 
and readings are to be taken when the graduations, the cross- 
hair, and its reflection are in line. In the late styles of this 





Fig. 71. — Buzby Hair-line Extensometer. Y\c. 72.— The RiehlIs Extensometer. 

instrument the disk is made of aluminium, with open spokes, 
to reduce its weight. 

To operate this instrument it is only necessary to clamp 
it to the specimen, to adjust the mirror and cross-hair, and 
then to revolve the disk by hand until the zero-line corre- 
sponds with the cross-hair and its reflection. Stress is then 
applied to the specimen, and readings taken as desired in the 
manner described. 

The Riehle' Extensometer. — The Riehle extensometer is 
a combination of compound levers which are attached to both 
sides of the specimen, and arranged so that one side carries a 
scale and the other a vernier. It is only mechanical in opera- 
tion, and can be used on specimens varying in length from 6 
to 8 inches. It is adjusted to the specimen by the clamp 
screws in the usual manner, and the ends of the graduations 
are then brought together at zero at both sides at the same 
time. Pressure is then applied to the specimen and the 



§82.] 



TES TING-MA CHINE A CCESSORIES, 



129 



readings taken in the same manner as any scale and vernier, 
the scale being graduated to thousandths and the vernier to 
ten thousandths. 

Johnson s Extensometer. — Johnson's extensometer, shown 
in Fig. 73, is a modification of the 
Strohmeyer, the elongation being de- 
noted by the motion of a needle over a 
graduated scale. The elongation for each 
side is shown separately, and the alge- 
braic sum of the two readings gives the 
total elongation. 

82. Thurston's Extensometer 

This extensometer was designed by Prof. 
R. H. Thurston and Mr. Wm. Kent, 
and was the first to employ two microm- 
eter-screws, at # equal distances from the 
axis of the specimen. These were con- 
nected to a battery and an electric bell 
in such a manner that the contact of 
the micrometer-screws was indicated by 
sound of the bell. The method of using 
this instrument is essentially the same 
as that of the Henning and Marshall instrument, to be 
described later. 

With instruments of this nature a slight bending in the 
specimen will be corrected by taking the average of the two 
readings. 

The accuracy of such extensometers depends on — 

1. The accuracy of the micrometer-screws. 

2. The screws to be compensating must be two in number, 
in the same plane, and at equal distances from the axis of the 
specimen. 

3. The framework and clamping device must hold the mi- 
crometers rigidly in place, and yet not interfere with the ap- 
plication of stress. 

83. The Henning Extensometer. — This instrument, which 
was designed by G. C. Henning and C. A. Marshall, is shown in 
Fig. 74- It is constructed on the same general principles as the 




Fig. 73.— Johnson's Exten- 
someter. 



no 



EXPERIMENTAL ENGINEERING^ 



[§83- 



Thurston Extensometer, but the clamps which are attached to 
the specimen are heavier, and are made so that they are held 
firmly in position by springs up to the instant of rupture. 
This extensometer is furnished with links connecting the two 
parts together. The links are used to hold the heads exactly 
eight inches apart, and are unhooked from the upper head 




Fig. 74.— The Henning Micrometer. 

before stress is applied to the specimen. The micrometer is 
connected to an electric bell in the same manner as the 
Thurston extensometer. 

Henning 's Mirror Extensometer \* — In 1896 Gus. C. Henning 
designed a mirror extensometer differing in several particulars 
from that of Bauschinger. The instrument is intended for 
accurate measurements of the extension or compression on 
both sides of the test-piece within the elastic limit, and is said 
to fulfil the following conditions: (a) It is applicable for 
measures of extension or compression, (b) Readings in either 
direction, negative or positive, can be taken without interrup- 
tion or adjustment. (•;) The instrument is free from changes 
of shape during the test, (d) There is neither slip nor play of 
the working parts. 

* See Transactions American Society Mechanical Engineers, vol. xviii. 






§84-] 



TEST1NGMA CHINE A CCESSORIES. 



131 



The instrument consists of two parts; the first is a telescope 
provided with levelling-screws, mounted on a horizontal and 
vertical axis and furnished with supports tor two linear scales, 
which may be arranged so that the reflection will show in 
mirrors attached to the specimen. The second part consists of 
a frame which can be fastened to the test-specimen near one 
end by opposite-pointed screws, and which is connected to 
spindles carrying the mirrors by spring side-bars. A portion 
of each mirror-spindle is double knife-edged, and when adjusted 




Fig. 75. — The Marshall Extensometer 



Fig. 76. — Jenning's Extensometei 



is brought in contact on one side with the test-piece, and on 
the other with the spring side-bar. The elongation of the 
test-piece causes an angular motion of the mirror, which in 
turn causes a multiplied motion of the reflection of the scale 
as seen from the telescope. The mirrors are so arranged that 
the reflections from both scales can be seen continually and 
without adjustment of the telescope, and the apparatus as a 
whole has fewer parts and is more readily adjusted than the 
Bauschinger. It is limited to a total elongation of about 0.04 
inch and hence is accurate only for measurements within the 
elastic limit. 

84. The Marshall Extensometer. — This extensometer, 
shown in Fig. 75> is the latest design of the late Mr. C. A. 
Marshall. Its principal difference from the Thurston exten- 



132 



EXPERIMENTAL ENGINEERING. 



[§85. 




Fig. 



77- 



someter is in the convenient form of clamps, which are well 
shown in the cut, and in the spring apparatus for steadying 
the lower part. 

The micrometer-screw used with this instrument has a 
motion of only one inch. When the motion exceeds the 
range of the micrometer-screws, the movable bars BP, B'P r 
are changed in position, and a new series 
of readings taken with the micrometer- 
screw. To facilitate the change of posi- 
tion of these bars, and allow the microme- 
ter-screw to return to zero at each change, 
the arrangement shown in Fig. 77 is 
adopted, which consists of a nut to which 
is attached a slotted taper-screw, on which 
screws a second nut, which serves to clamp the lower nut to 
the bar ; by turning the lower nut when clamped, the desired 
adjustment can be made. 

The following are the directions for use : 
Run wire (Fig. j6) from one terminal of battery to lower 
clamp at A, from B and B' to binding-post C on the electric 
bell, from the other binding-post marked D to switch E, and 
from there back to the other terminal of battery. 

To measure strain, screw up micrometer-screws at P and P' 
until each of them makes connection and bell rings; then take 
the readings on both sides. 

85. Boston Micrometer Extensometer. — This instru- 
ment consists, as shown in Fig. 78, of the graduated microm- 
eter-screw, reading in thousandths up to one inch, and having 
pointed extension-pieces attached, for gauging the distance 
between the small projections on the collars fastened to the 
specimen at the proper distance. These collars are made partly 
self-adjusting by the springs which help to centralize them. 
They are then clamped in place by means of the pointed 
set-screws on the sides, and measurements are made between 
the projections on opposite sides of the specimen and com- 
pared, to denote any changes in shape or variations in the 
two sides. 



86.] 



TESTING-MA CHINE A CCESSORIES. 



13. 



The Brown and Sharpe micrometer can readily be used with 
similar collars,thus forming an exten- 
someter ; .the accuracy of this form is 
considerably less than those in which 
the micrometers are fixed, but it 
will, however, be found with careful 
handling to give good results. 

Of the various extensometers de- 
scribed, the Paine, Buzby, Marshall, 
and Riehle are manufactured by 
Riehle Bros., Philadelphia ; the 
Thurston, by Olsen of Philadelphia ; 
the others, by the respective de- 
signers. 

86. Combined Extensometer 
and Autographic Apparatus. — An 
extensometer designed by the 
author, and quite extensively used 
in the tests of materials in Sibley 
College, is shown in Fig. 80 in ele- 
vation and in Fig. 81 in plan. In 
this extensometer micrometers of 
the kind shown in Fig. 22, Article 42, 
p. 60, with the addition of an exten- 
sion-rod for holding, are used. This 
rod sets into a socket A, which holds 
the micrometer in position. Read- 
ings are taken on the thimble B, as 
explained on p. 52. Connections are made with bell and 
battery at m, n, and m\ n', so that contact of the micrometer- 
screws is indicated by sound. The construction of the clamp- 
ing device is fully shown in the plan view, Fig. 81. 

The principal peculiarity of this extensometer consists in the 
addition of four pulleys, C lt C 2 , C % and C A , which are arranged 
so that a cord ab can be fastened at C 3 and passed down and 
around the pulley C lf thence over the guide-pulley W, Fig. 81, 
to pulley £T 2 , thence over the pulley C K , and thence to a paper 




Fig. 7 8. 



134 



EXPERIMENTAL ENGINEERING. 



[§86. 



drum. It is at once evident that any extension of the speci- 
men SS' will draw in the free end of the cord at twice the 
rate of the extension ; moreover, any slight swinging or rock- 
ing of the extensometer head will produce compensating 
effects on the length of the cord. By connecting the free end 
of the cord to a drum, the drum will be revolved by the stretch 




Fig. 80. 



Fig. 8i. 



of the specimen. As this work may be done against a fixed 
pull, there may be a uniform tension on the cord so that the 
motion of the drum would be uniform and proportional to the 
stretch. A pencil is moved along the axis of the drum pro- 
portional to the motion of the poise. 

An autographic device constructed in this way has given 
excellent diagrams, and in addition has served as an extensom- 
eter for accurate measurements of strain within the elastic 
limits. Wire has been used to connect extensometer to drum 
in place of the cord with success. A suggested improvement is 



§ 87-1 TESTING-MACHINE ACCESSORIES. I 35 

to rotate the drum by the motion of the poise, and to move 
the pencil by the stretch of the material, using two pencils, 
one of which is to move at a rate equal to fifty times the 
strain, the other at a rate equal to five times the strain ; thus 
producing two diagrams — one on a large scale, for use in deter- 
mining the strains during the elastic limit; the other on a 
small scale, for the complete test. 

87. Deflectometer for Transverse Testing. — Instru- 
ments for measuring the deflection of a specimen subjected to 
transverse stress are termed deflectometers. 

The deflectometer usually used by the author consists of a 
light metal-frame of the same length as the test-piece, and 
arched or raised sufficiently in the centre to hold a micrometer 
of the form used in the extensometer described in Article 86, 
above the point to which measurements are to be taken. In 
using the deflectometer it is supported on the same bearings 
as the test-piece, and measurements made to a point on the 
specimen or to a point on the testing-machine which moves 
downward as the specimen is deflected. This instrument 
eliminates any error of settlement in the supports. A steel 
wire is sometimes stretched by the side of the specimen, and 
marks made on the specimen showing its original position with 
reference to the wire. The deflection at any point would be 
the distance from the mark on the specimen to the corre- 
sponding point on the wire. The cathetometer, see Article 43, 
page 63, is very useful in determining the deflection in long 
specimens. The deflection is often measured from a fixed 
point to the bottom of the specimen, thus neglecting any error 
due to the settlement of the supports. One of the most use- 
ful instruments of this kind is made by Riehle Bros., and is 
shown, together with the method of attachment, in Fig. 82. 




Fig. 



CHAPTER V. 
METHODS OF TESTING MATERIALS OF CONSTRUCTION. 

Standard Methods. — The importance of standard 
methods of testing material can hardly be overestimated if it 
is desired to produce results directly comparable with those 
obtained by other experimenters, since it is found that the re- 
sults obtained in testing the strength of materials are affected 
by methods of testing and by the size and shape of the test- 
specimen. To secure uniform practice, standard methods for 
testing various materials have been adopted by several of the 
engineering societies of Germany and of the United States, as 
well as by associations of the different manufacturers. The 
general and special standard methods adopted by these asso- 
ciations form the basis of methods described in this chapter. 

88. Form of Test-pieces. — The form of test-pieces is 
found to have an important bearing on the strength, and for 
this reason engineers have adopted certain standard forms to 
be used. The form recommended by the Committee on 
Standard Tests and Methods of Testing, of the American 
Society of Mechanical Engineers is as follows:* 

" Specimens for scientific or standard tests are to be pre- 
pared with the greatest care and accuracy, and turned accord- 
ing to the following dimensions as nearly as possible. The 
tension test-pieces are to have different diameters according to 
the original thickness of the material, and to be, when ex- 
pressed in English measures, exactly 0.4, 0.6, 0.8, and 1.0 inch 
in diameter; but for all these different diameters the angle, but 

* See Vol. XL of Transactions. 

136 



§88.] 



TESTING MATERIALS OE CONSTRUCTION. 



17 



not the length, of the neck is to remain constant. This neck 
is a cone, not a fillet connecting the shoulders and body. The 
length of the gauged or measured part to be 8 inches, of the 
cylindrical part 8.8 inches. The length of the coned neck to 
be 2i times the diameter, increasing in diameter from the 
cylindrical part to \\ times the cylindrical part. The shoul- 
ders to have a length equal to the diameter, and to be con- 
nected with a round fillet to a head, which has a diameter 
equal to twice that of the cylinder, and a length at least ij 
the diameter. 

Fig. 83 shows the form of the test-piece recommended 
for tension ; the numbers above the figure give dimensions in 



S-25-4-20-4* 50— "^ 2 20 millimetres-—*- 4" 5 <> *< 



\r-i- 



) r\— f— • 



* 



z± 



20>|*-25-* 



Millet 0.1 R. 

! U.fr»+-- — 2 4 1 *"""" ' 8.8-inches 4« 2 » <0.8+--l— »J 

Fig. 83.— Standard Test-piece in Tension. 



millimeters, those below in inches. For flat test-pieces the 
shape as shown in Fig. 84 is recommended : such specimens 



-*f-i2*fc 



i— . 



n 



-^12*- 

\J- 



|*W 8.8- 



rv 



Fig. 84.— Test-piece for Flat Specimens. 

are to be cut from larger pieces ; the fillets are to be accurately 
milled, and the shoulders made ample to receive and hold the 
full grip of the shackles or wedges. 

The length for rough bars is to remain the same as for fin 
ished test-pieces, but the length of specimen from the gauge- 
mark to the nearest holder is to be not less than the diameter 



138 



EXPERIMENTAL ENGINEERING. 



[§89. 



of the test-piece if round, or one and a half times the greatest 
side if flat. 

For commercial testing the standard form cannot always 
be adhered to, and no form is recommended.* 

It is recommended in all cases that the specimens be held 
by true bearing on the end shoulders, as gripping or holding 
devices in common use produce undesirable effects on the 
cylindrical portion of the specimen. 

The forms of test-specimens which have been heretofore 
used are somewhat different from the standards recommended. 
These forms are shown in Fig. 85, No. 1 to No. 5, and are as 
follows : 



No. i. Square or flat bar. at 
rolled. 

J 6 To 20- 

No. 2. Round bar, as roiled. 

No. 3. Standard shape for flats of 
,;'.,;■ squares. Edges must 

< B 2a ^ be smooth and true. Fil- 

lets, one half inch radius. 

"i. g ^, Specimens not over three 

BETWEEN FILLETS inches wide. 

1 61 20 ^ 

No. 4. Standard shape for rounds. 
- gtt -,. 

ft. 11 

No: 5. Government shape for 
marine-boiler plates only. 
Not in general use, as it 
gives too high a test. 

Fig. 85.— /orms of Specimen for Tensile Strains formerly used. 

$9. Test-pieces of Special Materials. — Wood. — Wood is 
a difficult material to test in tension, as the specimen is likely 
to be crushed by the shackles or holders. The author has had 
fairly good success with specimens, made with a very large 
bearing-surface in the shackles, of the form shown in Fig. 84, 




* A discussion of the effect of varying proportion of test-pieces is given in 
Thurston's ■• Text-book of Materials," pages 356-7- 



§8 9 -] 



TESTING MATERIALS OF CONSTRUCTION, 



'39 



page 137 for flat specimens, but with the breadth of the shoul- 
ders or bearing-surfaces increased an amount equal to one half 
the diameter of the specimen over that shown in Fig. 84. 

Cast-iron. K — Cast-iron specimens of the usual or standard 
forms are very likely to be broken by oblique strains in tension 
tests much before the true breaking-point has been reached. 
To insure perfectly axial strains Riehle Bros, propose a form 
of specimen shown in Fig. 86, A, B, and C, cast with an enlarged 






Fig. 86.— Proposed Form for Cast-iron Specimens. 



head, the projecting portion of which, as shown in C, has 
a knife-edge shape. The specimen is carried in holders o«" 
shackles, A and B, which rest on knife-edges extending 
at right angles to those of the specimen. This permits 
free play of the specimen in either direction, and renders 
oblique strains nearly impossible. 

Chain, — In the case of chain, large links are welcjed at the 
ends, as shown in Fig. 87 ; these are passed through the heads 
of the testing-machine and held by pins. 



v 1 -^ liyi^riiiTfeni' ^tj 



Fig. 87.— Chain Test-piece. 



4o 



EXPERIMENTAL ENGINEERING. 



L§89- 



Hemp Rope. — A similar method is used in testing hemp 
rope, the specimen being prepared as shown in Fig. 88. 




Fig. 



-3.o?e Test-piece. 



Special hollow conical shackles have also been used for hold- 
ing the rope with success. 

Wire Rope. — Wire-rope specimens may be prepared as 
shown in Fig. 89, or they may be prepared by pouring a mass 



Fig. 89.— Wire-rope Test-piece. 

of melted Babbitt metal around each end and moulding into a 
conical form, taking care that the rope is in the exact centre 
of the metal. 

Cement. — Cement test-pieces for tension are made in moulds 
and permitted to harden for some time before being tested. It 
is found that the strength is affected by the form 6f the speci- 




Fig. 90. — Old C E. Standard Specimen for Cement. 

men, by the amount of water used, and by the method of mix- 
ing the cement. To get results which may safely be compared, 
it is necessary to have the test-specimens or briquettes of 
exactly the same form, and pulled apart in shackles or holders 



5 89.] 



TESTING MATERIALS OF CONSTRUCTION. 



I 4 I 



which exert no side strain whatever, and the strain applied uni- 
formly and without any jerky motion. Various standard forms 
of briquettes have been employed; the one most used in America 
prior to 1904 is shown full size in Fig. 90. That recently adopted 
is shown half size in Fig. 94. 




Fig. 91. — Cement Moulds and Briquettes. 

The form of the mould for making the briquettes, and the 
holders or shackles generally used, are shown in Figs. 91 to 93. 

J 

DETAILS FOR GANG MOULD 

Fig. 92. 






FORM OF CLIP DETAILS FOR BRIQUETTE 

Fig. 93. Fig. 94. 

Standard Clip and Briquette adopted by the American Society for Testing 
Materials, 1904. 

The gang-mould, as shown in Fig. 92, consisting of several moulds 
united in one construction, is preferred when numerous briquettes 
are to be made. 



142 EXPERIMENTAL ENGINEERING. [§ 90. 

Standard revised specifications for testing cement were adopted 
by the American Society of Civil Engineers and approved by the 
American Society of Testing Materials, 1904. The form of 
briquette adopted is shown in Fig. 94, which differs from the 
earlier form principally in the use of rounded instead of sharp 
corners, as noted by comparing Figs. 90 and 94. 

90. Compression-test Specimens — Test-pieces. — Test- 
pieces are in all cases to be prepared with the greatest care, to 
make sure that the end surfaces are true parallel planes normal 
to the axis of the specimen. 

1. Short Specimens. — The standard test specimens are to be 
cylinders two inches in length and one inch in diameter, when 
ultimate resistance alone is to be determined. 

2. Long Specimens. — For all other purposes, especially when 
the elastic resistances are to be ascertained, specimens one inch 
in diameter and ten or twenty inches long (see No. 2, Fig. 85) 
are to be used. Standard length on which strain is to be meas- 
ured is to be eight inches, as in the tension-tests. Greatest care 
must be taken in all cases to insure square ends and that the 
force be applied axially. 

The specimens are to be marked and the compression meas- 
ured as explained for tension- test pieces, page 126. 

91. Transverse-test Specimens. — For standard trans- 
verse tests, bars one inch square and forty inches long are to be 
used, the bearing blocks or supports to be exactly thirty-six 
inches apart, centre to centre. For standard or scientific tests 
of cast-iron, such bars are to be cut out of a casting at least two 
inches square or two and a quarter inches in diameter, so as to 
remove all chilling effect. For routine tests, bars cast one inch 
square may be used, but all possible precautions must be taken 
to prevent surface-chilling and porosity. 

Test-bars of wood are to be forty inches in length, and three 
inches square in section. 

92. Torsion-test Specimens. — For standard tests, cylin- 
drical specimens with cylindrical concentric shoulders are to be 
used; the two are connected by large fillets. The specimen 



§93*1 TESTING MATERIALS OF CONSTRUCTION. 1 43 

is to be held in the chuck or heads of the machine by three 
keys, inserted in key-ways \ inch deep, cut in the shoulder. 

93. Elongation — Fracture. — The character of the fracture 
often affords important information regarding the material. 
The structure of the fractured surface should be described as 
coarse or fine, either fibrous, granular, or crystalline. Its form, 
whether plane, convex, or concave, cup-shaped above or below, 
should in each case be stated. Its location should be accu- 




19 18 17 16 15 14 13 



Fig 95. 

*ately given, from marks on the specimen one half inch or less 
apart. The reduction of diameter which accompanies fracture 
should be accurately measured. Accompanying the report 
should be a sketch of the fractured specimen. 

Fracture occurs usually as the result of a gradual yielding 
of the particles of the specimen. The strain, so long as the 
.stress is less than the maximum load, is distributed nearly uni- 
formly over the specimen, but after that point is passed the dis- 
tortion becomes nearly local ; a rapid elongation with a corre- 
sponding reduction in section is manifest as affecting a small 
portion of the specimen only. This action in materials with 
sensible ductility takes place some little time before rupture; 
in very rigid materials it cannot be perceived at all. This 
peculiar change in form is spoken of as " necking." 

The drawing Fig. 95 shows the appearance of a test speci- 
men in which the " necking " is well developed. Rupture 
occurs at b— b, a point in the neck which may be near one 
end of the specimen. 

In order to measure the elongation of the specimen fairly, a 
correction should be applied, so that the reduced elongation 
shall be the same as though the stretch either side of the point 



144 EXPERIMENTAL ENGINEERING. [§ 94* 

of rupture were equal. This can only be done by dividing up 
the original specimen into equal spaces, each of which is marked 
so that it can be identified after rupture. 

Supposing that twenty spaces represent the full length be- 
tween gauge-marks : then if the rupture be nearest the mark 
o, Fig. 95, three spaces from the nearest gauge-mark, the 
total length to compare with the original length is o to 3 on 
the right, plus o to 10 on the left, plus the distance 3 to 10 
on the left. These spaces are to be measured, and the sum 
taken as the total length after rupture. The stretch is the 
difference between this and the original length ; the per cent 
of stretch, or elongation, is the stretch divided by the original 
length. This method is stated in a general form as follows : 

Divide the standard length into m equal parts, and repre- 
sent the number of these parts in the short portion after rupture 
hy s. Note two points in the long portion, A and B, at s and 
^m divisions respectively from the break. Lay the parts to- 
gether, and measure from the gauge-mark in the short por- 
tion to point A. This distance increased by double the 
measured distance from A to B gives the total length after 
rupture. Subtract the original length to obtain the total elon- 
gation: thus the elongation of the standard m parts will be 
obtained as though the fracture were located at the middle 
division. 

94. Strain-diagrams. — The results of measurements of 
the strain should be represented graphically by a curve 
termed a strain-diagram. 

Strain-diagrams are drawn (see Art. 46, page 70) by taking 
the loads per square inch (/>) as ordinates, and the relative 
stretch or strain (e) to a suitable scale as abscissae. The curve 
so formed will be a straight line from the origin to the elastic 
limit, and the tangent of the angle that it makes with the axis 
of X {p -f- e = E) will be proportional to the modulus of elas- 
ticity. The area included between the axis of X and that por- 
tion of the curve preceding the elastic limit will represent the 
Elastic Resilience or work done by the resistance of the 
material to that point. 



§95*] TESTING MATERIALS OF CONSTRUCTION. I45 

Autographic Strain-diagrams are drawn automatically 
on a revolving drum. In most machines the drum is revolved 
by the stretch of the material and a pencil is moved parallel 
to its main axis and proportional to the motion of the weigh- 
ing poise, although in some devices for drawing autographic 
diagrams the drum is actuated by the poise motion, the pencil 
by the stretch. The Olsen autographic apparatus is described 
in Article 71, Figs. 56 to 60, page 11 1. This apparatus is very 
perfect in all its details, and produces a diagram similar to 
that shown in Fig. 96. 

The ordinates on this diagram are proportional to the 
load, the abscissae to the strain. The lines are straight and 
nearly vertical until the yield-point ; then for a time the strain 
rapidly increases, with little increase of stress as shown by the 
line of stress ; this is followed by an increase of both stress and 
strain, until the point of maximum loading is reached. After 
passing the elastic limit the strain increases very rapidly, the 
stress but little. 

The autographic attachment is a valuable addition to a 
testing-machine, especially if its use does not interfere with 
the measurement by micrometers ; but if the scale of the dia- 
gram does not exceed five or ten times that of the actual 
strain, it is of value only in showing the general character of 
the strain, and is not to be considered of value in obtaining 
coefficients or moduli within the elastic limit. 



TENSION TESTS. 

95. Objects of Tension Tests. — Tension tests are con- 
sidered valuable as affording information of the qualities of 
material, and a certain tensile strength is required of nearly 
all materials used, even though in practice they may be sub- 
jected to different kinds of strain. The breaking-strength is 
frequently specified within limits, and is to be accompanied with 
a certain amount of ductility. 

Directions for Tension Tests. — Examine the test-piece care. 



§950 



TESTING MATERIALS OF CONSTRUCTION. 



14/ 



fully for any flaw, defect, irregularity, or abnormal appearance, 
and see that it is of correct form and carefully prepared. In- 
dentations from a hammer often seriously affect the results. 
In wood specimens, abrasions, slight nicks at the corners, or 
bruises on the surface will invariably be the cause of failure. 

Next, carefully measure the dimensions, record total length, 
gauge-length (or length on which measurements of strains are 
made), also form and dimensions of shoulders. Divide the 
specimen between the gauge-marks into inches and half inches, 
which may be marked with a special tool, or by rubbing chalk 
on the specimens and marking each division with a steel scratch. 




Fig. 97. — Laying-off Gauge. 



A special gauge as shown in Fig. 97 is convenient for this pur- 
pose. These marks serve as reference points in measuring the 
elongation after rupture, and this elongation should be meas- 
ured, not from the centre of the specimen, but from the point 
of rupture either way, as explained in Art. 93, page 143. 

See that the testing-machine is level and balanced before 
each test ; insert the specimen in a truly axial position in the 
machine by measuring carefully its position in two directions, 
and by applying a level. Calculate from the known coefficients 
of the material the probable load at elastic limit. Take one 
tenth of this as the increment of load. The Committee on 
Standard Tests, American Society of Mechanical Engineers, 
recommend that the increment be one half or one third that of 
the probable load at the elastic limit, thus giving larger strains 
but fewer observations. Apply one increment of load to the 
specimen before measurements of elongation are made, since by 
loading specimens up to 1000 or 2000 pounds per square inch 
the effect of initial errors, such as occur generally at the com- 
mencement of each test, are lessened. The auxiliary apparatus 



148 



EXPERIMENTAL ENGINEERING. 



[§0. 



adjusts itself somewhat during this period of loading, and the 
specimen assumes a true position should any slight irregularity 
exist. 

96. Attachment of Extensometer. — Attach the auxiliary 
apparatus for measuring stretch, or obtaining autographic dia- 
grams. The method of attaching extensometers will depend 
on the special form used (see Articles 80 to 86), but this act 
should always be carefully performed, and the specimen exactly 
centred in the extensometer, and the gauge-points arranged 
8 inches apart. The following directions for applying and using 
the Henning extensometer will serve to show the method to be 
used in all cases. 

The Henning extensometer (see Article 83, Fig. 74, page 
130) is attached and used as follows: Before attaching the in- 
strument, adjust the knife-edges in the clamps by means of the 
two milled nuts so that they are equally distant from the 
frame and not so far apart as the diameter of the test-piece. 
Then, since the springs acting on the knife-edges are of equal 
strength, the instrument will adjust itself in the plane of the 
screws symmetrically with respect to the test-piece. Advance 
or withdraw the set-screws until their points are equally 
distant from the frame and far enough apart to admit the test- 
piece. 

Separate the upper portion of the instrument, put it around 
the test-piece (already inserted in the machine) near the upper 
shoulder, with the smaller part to the right, force together and 
fasten securely. Advance the set-screws simultaneously until 
their points indent the test-piece. Separate the lower portion, 
put it around the test-piece with the vertical scales to the front, 
force together and secure. Hang the links on the proper bear- 
ings on both portions of the instrument. Then advance the 
set-screws as above. Throw the links out, take readings of the 
micrometers, apply the first increment of load, and proceed 
with the test as directed. To read the micrometers make the 
electrical connections ; advance one micrometer until the bell 
rings announcing contact, back off barely enough to stop ring, 
ing, and advance the other until the bell rings. Back off as 



§ 9 8 -] TESTING MATERIALS OF CONSTRUCTION. 1 49 

before, and read both micrometers. The vertical scale and the 
micrometer head are graduated so that readings to i-o-$nF inch 
can be obtained directly. 

97. Tension Test. — The test is made by applying the 
stress continuously and uniformly without intermission until 
the instant of rupture, only stopping at intervals long enough 
to make the desired observations of stretch and change of 
shape. The stress should at no time be decreased and re- 
applied in a standard test, but should be maintained continu- 
ously. The auxiliary apparatus for measuring strain must be 
removed before rupture takes place, except it is of a character 
not likely to be injured. It should usually be taken off very 
soon after the elastic limit is passed ; although for ductile 
material it may be left in place for a longer time after the 
elastic limit has been passed than for hard and brittle materials. 
The material is then to be loaded until fracture takes place, 
keeping the beam floating, after which the distortion for each 
part is to be measured by comparison with the reference divi- 
sions on the test-piece, measured from the point of rupture as 
previously explained. It is to be noted that measurements 
within the elastic limit are of especial importance, since materials 
in use are not to be strained beyond that point. 

98. Report. — Remove the fractured piece from the machine ; 
make measurements of shape, external and fractured surface ; 
give time required in making the test.* When fracture is cup- 
shaped, state the position of cup — whether in upper or lower 
piece. 

In recording the results of tests, loads at elastic limit, at 
yield-point, maximum, and instant of rupture are all to be noted. 

The load at elastic limit is to be that stress which produces 
a change in the rate of stretch. 

The load at yield-point is to be that stress under which the 
rate of stretch suddenly increases rapidly. 



* See Report of Committee on Standard Tests, Vol. XL, Am. Society Mech. 
Engrs. 



150 EXPERIMENTAL ENGINEERING. [§ 98. 

The maximum load is to be the highest load carried by the 
test-piece. 

The load at instant of rupture is not the maximum load 
carried, but a lesser load carried by the specimen at the instant 
of rupture. 

In giving results of tests it is not necessary to give the load 
per unit section of reduced area, as such figure is of no value; 
(1) because it is not always possible to obtain the load at in- 
stant of rupture ; (2) because it is generally impossible to obtain 
a correct measurement of the area of section after rupture; 
(3) lastly, because the amount of reduction of area is principally 
dependent upon local and accidental conditions at the point of 
rupture. The modulus or coefficient of elasticity is to be 
deduced from measurements of strain observed between fixed 
increments of load per unit section ; between 2000 pounds per 
square inch and 12,000 pounds per square inch; or between 
1000 pounds per square inch and 11,000 pounds per square 
inch. With this precaution several sources of error are 
avoided, and it becomes possible to compare results on the 
same basis. 

In the report describe the testing-machine and method of 
testing, form and dimensions of specimen, character and posi- 
tion of rupture. Calculate coefficients of elasticity, maximum 
strength, breaking-strength, strength at elastic limit, and resili- 
ence, and submit a complete log of test. Also, draw a strain- 
diagram on cross-section paper ; make a sketch of surface of 
rupture. The curve of stress and strain is to be drawn as 
follows : Plot a curve of stress and strain up to a point beyond 
the elastic limit, using for ordinates values of /, on the scale 
I div. == 2000 lbs. per sq. in., and for abscissae values of e, on 
the scale 1 div. = 0.0001"; compute E and/. Then plot the 
complete curve of stress and strain to the point of rupture, 
using scales of I div. = 10,000 lbs. per sq. in., and 1 div. = 0.01 
inch for ordinates and abscissae, respectively. 

A blank form for the log is shown below, which is to be 
filled out and filed. On this log is to be entered, value of the 



§98.] 



TESTING MATERIALS OF CONSTRUCTION. 



151 



modulus of elasticity, load at elastic limit, character of rupture, 
area of least section, and measurements between each mark 
made on the specimen. 

The following form is used by the author for both tension 
and compression tests : 



Test of by. 

Kind of Test 

Material from 

Machine used 

Time of Testing min. 



Date 189 

Tempt degrees F. 



No. 



Load. 


Micrometer- 
readings. 




Extension. 




Actual. 
P 


Per sq. in. 
P 


I 


II 


Mean. 


Actual. 
k 


Difference. 


Per in. 

e 



















Modulus 

Elasticity. 

E 



Original length in. Diameter in. Area sq. in. 

Final " in. Diameter in. Area. " 

Form of section Fracture: position ; character.. 

Moduli: resilience ; breaking-strength 

Load per sq. inch: elastic limit max breaking 

Equivalent elongation for 8 inches inches per cent. 

Elongation Reduction area per cent. Local elongation each 

half-inch, from top, 1st ; 2d ; 3d ; 4th ; 5th ; 

6th ; 7th ; 8th ; 9th ; 10th ; nth ; 12th ...; 

13th ; 14th ; 15th ; 16th 



The following form, from Vol. XL Trans. American Society 
Mech. Engineers, is excellent for reporting the principal 
results of a series of tests. Attention is called to the full 
descriptions accompanying the report. 



152 



EXPERIMENTAL ENGINEERING. 



L§98. 



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§98.] 



TESTING MATERIALS OF CONSTRUCTION. 



153 



Prof. G. Lanza of the Massachusetts Institute of Tech- 
nology uses the following forms for log and report of tension- 
tests : 



TENSION-TEST. 
Date . . . 



No 

Specimen , 

Length between clamps Tested by. 

Original section 



Loads. 


Micrometer-readings. 


Mean. 


Differences. 


Actual. 


Per sq. in. 


z 


2 


1 


2 


Actual. 


Per inch. 



















Remarks. 



Fractured section Breaking-stress per sq. in. fractured section., 

Reduction of area of cross-section Modulus of elasticity 

Ultimate extension Modulus of elastic resilience 

Cross-section at maximum load. ....... Modulus of ultimate resilience. 

Tensile limit per sq. in , 



REPORT. 



No 

Specimen 

Length between clamps, 

Original section, 

Elastic limit, 

Breaking-load, 

Fractured section, 

Reduction of area of cross-section, . . 

Ultimate extension, 

Breaking-stress per square inch fractured 

Modulus of elasticity, 

Signed 



Date 




?54 



EXPERIMENTAL ENGINEERING. 



L§9£> 



COMPRESSION-TESTS. 



99. Methods of Testing by Compression. 1. Short 
Pieces : Method of Testing. — In case of short pieces, measure- 
ments of strain cannot be made on the test-piece itself, but 
must be made between points on the heads of the testing- 
machine. It is necessary to ascertain and make a correction 
for the error due to the yielding of the parts of the testing- 
machine. This is done as follows: Lower the moving-head 
until the steel compression-plate presses on the steel block in 
the lower platform with a force of about 500 pounds. Attach 
the micrometers to the special frame, which is supported by 
the upper platform, and read to a point on the movable head. 
With load at 500 pounds, read both micrometers. Apply loads 
by increments of 1000 pounds up to three fourths the limit of 
the machine, taking corresponding readings. Plot a curve of 
loads and deflections with ordinates 1 long division = 1000 
pounds, and abscissae I long division = 0.001 inch. From 
this curve obtain corrections for the deflections caused by the 
loads used in the compression-test. In making the test calcu- 
late the increment of load as explained for tensile strain, Arti- 
cle 98. Conduct the experiment in the same manner as for 
tension, except that the stress is applied to compress instead 
of to stretch the specimen. If the material tested is hard or 
brittle, as in cast-iron, care should be taken to protect the 
person from the pieces which sometimes fly at rupture. 

Report and draw curve as for tension-tests, and in addition 
show why brittle material breaks in planes, making angles of 
about 45 with the axis of the piece ; compare the results 
obtained for wrought-iron in compression with those obtained 
in tension. 

2. Long Pieces : Method of Testing. — In this case the exten- 
someters used for tension-tests can be connected directly to 
the specimen, and the measurements taken in substantially the 
same May, except that the heads of the extensometer will 
approach instead of recede from each other ; this makes it 



§ IOO.] TESTING MATERIALS OE CONSTRUCTION. 15$ 

necessary to run the screws back each time after taking a meas- 
urement a distance greater than the compression caused by 
the increment of load. In case large specimens are tested 
horizontally, initial flexion is to be avoided by counterweight- 
ing the mass of the test-piece. 

Calculate the increment of load as one tenth the breaking- 
load given by Rankine's formula, Article 51, page 74. Apply 
the first increment and take initial reading of micrometers; 
continue this until after the elastic limit has been passed, after 
which remove the extensometer, and apply load until rupture 
takes place. Protect yourself from injury by flying pieces. 
Compute the breaking coefficient C by Rankine's formula, and 
compare with the usual results. 

Compute the modulus of elasticity by Euler's formula: 

(1) P," = £1^ + /'" (Church," Mechanics of Materials," p. 366). 

(2) E = t"*P " -T- jtV. /"=■/- \". (3) £ = (/- VJP' ~ ?t*L 

Also by the method used in testing short specimens. 

In the above approximate formula the notation is the same 
as in Article 48, page 72. 

Note in the report, load at elastic limit, yield-point, and 
ultimate resistance, as well as increase of section at various 
points, and total compression calculated as explained for 
tension. 

Submit a strain-diagram, and follow the same general direc- 
tions as prescribed in the report for tensile strain, Article 98. 

TRANSVERSE TESTS. 

100. Object. — This test is especially valuable for full-sized 
pieces tested with the load they will be required to carry in 
actual practice. 

The deflections of such pieces, with loads at centre or in 
various other positions, afford means of computing the coeffi- 
cients of elasticity and the form of the elastic curve. 

Method of Testing. — Arrange the machines for such tests 



156 EXPERIMENTAL ENGINEERING. [§ IOO. 

by putting in the supporting abutments, and by arranging the 
head for such tests, or else by using the special transverse 
testing-machine. 

In this experiment the test-piece is usually a prismatic 
beam, 3 feet long (see Article 91, page 142), and it is supported 
at both ends, the stress being applied at the centre. The 
same data are required to be observed as in the preceding 
experiment, viz., loads and deflections, or stresses and corre- 
sponding strains. 

Sharp edges on all bearing-pieces are to be avoided, and 
the use of rolling bearings which move accurately with the 
angular deflections of the ends of the bars are recommended ; 
otherwise the distance between fixed supports measured along 
the axis of the specimen is continually changing. 

Place the test-bar upon the supports, and adjust the latter 
36 inches apart between centres, and so that the load will be 
applied exactly at the middle. Obtain the necessary dimen- 
sions, and calculate the probable strength at elastic limit and 
at rupture by means of the formula/ = Wle -^ 4L (See Arti- 
cle 52, page 78.) Adjust the specimen in the machine in a 
horizontal plane, and apply the stress at the centre normal 
to the axis of the specimen, and in a plane passing through 
the three points of resistance. 

Measure the deflections at the centre from a fixed plane 
or base, allowing for the settling of the supports, or by the 
special deflectometer (see Article 87, page 1 3 5), from which 
compute the coefficient of resilience and the modulus of 
elasticity. 

Balance the scale-beam with the test-bar in position and 
the deflectometer lying on the platform. Set the poise for one 
increment of load and apply stress until the beam tips. Place 
the poise at zero, and balance by gradually removing the load. 
Place the deflectometer in position on the supports, and with 
the micrometer at zero make contact and record zeio-reading 
and zero-load. 

Apply the load in uniform increments equal to about one 
fifth the calculated load for the elastic limit, stopping only 



§ IOI.] TESTING MATERIALS OF CONSTRUCTION. 



157 



long enough to measure the deflections. Wrought-iron is to 
be strained only until it has a sensible permanent set, but cast- 
iron and wood are to be tested to rupture. Wood specimens 
generally rupture on one side only : in that case turn over and 
make complete test as in the first instance. 

IOI. Form of Report. — In the report describe the ma- 
chine, method of making test, form of cross-section, peculi- 
arities of the section, and make a sketch showing position and 
form of rupture. Submit a complete log of the test, together 
with drawing of the elastic curve, to be filed for permanent 
record. The following is a form for data and results of a 
transverse test : 



DATA OF TRANSVERSE TEST OF, 



Form of cross-section .... 

Length between supports ins. 

On Testing-machine. 

Time hrs mins. 



Date Observers: 





Load 
W. 


Deflection. 


Remarks. 


No. 


Reading. 


Net. 













REPORT OF TRANSVERSE TEST. 



Material , 

Form 1 

Composition Specific Gravity 

Load A pplied 

\ estinn machine 

Time hrs min. 

pate ,189 Observers:^ 



Wt. per cu. ft ?bs. 



i 5 8 



EXPERIMENTAL ENGINEERING. 



[§ 101. 



Dimensions. 


Symbol 


| 

i 

c 
o 

'& 
•c 

E 

a 




Length 

Diameter 

Breadth 


in. 

in. 

in. 


/ 

D 
b 
h 
e 
I 




Height 


in. 

in. 














Load. 


Actual. 


Reduced per sq. in. 
in Outer Fibre. 




Elastic limit 
























Deflection. 
















I 

3 




' 


Modulus of elasticity 






£ 


Modulus of resilience 




ft. lbs. 


"o 


Remarks: 






JS 
o 

V 

M 



The following forms are used by Prof. Lanza in the labora- 
tory of the Institute of Technology for log and report of trans 
verse test : 



LOG. 
Date 



No 

Specimen 

Span Wt. of beam 

Position of load 

Tested by 



Wt. of yoke, etc.... e 





Loads. 


Micrometer-readings. 


Mean. 


Differences. 


Remarks. 




i 


2 


I 


2 





















Modulus of elasticity 

Modulus of rupture (including weight of beam). 
Maximum intensity of longitudinal shear 



§ 102.] TESTING MATERIALS OF CONSTRUCTION. 



159 



REPOR' 
Date.. 



No 

Specimen 

Span, 

Dimensions, 

Weight of beam, . . . , 
Weight of yoke, etc., . . . 

Deflection, 

Modulus of elasticity, . . . 
Modulus of rupture (including weight of beam), 
Maximum intensity of longitudinal shear, . . 
(Signed) 

102. Elastic Curve. — The object of this experiment is to 
determine the coefficient and moduli of the material, by loads 
less than that required at the elastic limit. The required 
general formulae are to be found in Art. 52, page 77- A table 
of deflections corresponding to various centre loads is to be 
found on page 79. The beam is to be supported at both ends 
on rounded supports or on rollers. The loads consist of weights 
of known amount that can be suspended at various points. 

Apparatus needed. — Cathetometer or other suitable instru- 
ment for measuring deflection. 

Directions. — Obtain dimensions of beam, compute moment 
of inertia of cross-section ; note material of beam, and com- 
pute probable deflection and corresponding load at elastic 
limit. 

Carefully divide the length of the beam into equal parts, 
and mark these divisions on the centre-line of the beam. With 
no load on the beam, take cathetometer-readings of each point, 
then apply successive increment of loads, each equal to one 
fifth the £ robable load at the elastic limit, and take correspond- 
ing readings of the cathetometer. From readings, obtain 
the deflections for each point, and plot the elastic curve. 
Compute the deflections for the corresponding points from the 
formula, using tabulated values of E, and plot the correspond- 
ing theoretical curve. Make deductions concerning the rela- 
tion of the two curves. 



160 EXPERIMENTAL ENGINEERING. [} IO3 

The above experiment is to be performed with the load at 
center, and again with the load at a point one fourth or one 
third the length of the beam. 

Similar experiments may be performed on beams fixed at 
one end, or fixed at one end and supported at the other. 

TORSION-TEST. 

103. Object. — The object of this experiment is to find the 
strength of the material to resist twisting forces, to find its 
general properties, and its moduli of rigidity and shearing, 
strength. 

Thurston's Machine. — The special directions apply only to 
Thurston's torsion-machine (see Article 73, Figs. 61 and 62, 
page 114). In the use of the machine the constants are first ob- 
tained, the test-piece inserted between the jaws of the 
machine, stress applied, and the autographic strain-diagram 
obtained. This diagram is on a iarge scale, and gives quite 
accurate measures of the stresses or loads. The diagram is, 
however, drawn by attachment to the working parts of the 
frame, and consequently any yielding of the frame or slipping 
of the jaws appears on the diagram as a strain or yield of the 
specimen. The angular deformation a, as obtained from the 
diagram, is likely to be too great, especially within the elastic 
limit. This error should be determined in each test by attach- 
ing index arms at each end of the specimen, and corrections 
made to the results obtained from the diagram. 

The characteristic form of diagram given by the torsion- 
machine is shown in Fig. 98, in which the results of tests of 
several materials is shown. In the above diagrams* the ordi- 
nates are moments of torsion (Pa), the abscissae are develop- 
ments of the angle of torsion (a). The value of one inch of 
ordinate is to be found by measuring the ordinate correspond- 
ing to a known moment of torsion, and the abscissa corre- 

* See " Mechanics of Materials," page 240, by I. P. Church. Published by 
Wiley & Son, N. Y. 



I04-] TESTING MATERIALS OF CONSTRUCTION. 



:6i 



sponding to one degree of torsion is to be calculated from 
the known radius of the drum. Knowing these constants, 
numerical values can readily be obtained, and the coefficients 
of the strength of the material can be computed. 

During the test, relax the strain occasionally : if within the 
elastic limit, the diagram will be retraced ; but if beyond that 




limit, a new path is taken, called an " elasticity " line by 
Thurston, which is in general parallel to the first part of the line, 
and shows the amount of angular recovery BC y and the per- 
manent angular set OB. 

104. Methods of Testing by Torsion with Thurston's 
Autographic Testing-machine. (See Articles 55 and 73.) 

Method. — Determine first the maximum moment of the 
pendulum. This may be done by swinging the pendulum so 
that its centre-line is horizontal, supporting it on platform- 
scales and taking the weight and the distance of the point ot 
support from the centre of suspension of the pendulum. The 
product of these two quantities is the maximum moment of 
the pendulum. Make three determinations, using different 
lever-arms, and take the mean for the true moment of the 
pendulum. A correction for the friction of the journal of the 
pendulum must be made. When hanging vertically, measure 
with a spring-balance, inserted in the eye near the bob, the 
force necessary to start the pendulum. Add this moment to 
that obtained above, and the result is the total maximum 
moment of the pendulum. From this the value of the mo 
ment for any angular position may be calculated. 



1 62 



EXPERIMENTAL ENGINEERING. 



[§104 



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I 105.] TESTING MATERIALS OF CONSTRUCTION. 1 6 



Note the variation of the pencil-point between the vertical 
and the horizontal positions of the pendulum. This distance 
laid down on the F-axis of the record-sheet corresponds to 
the maximum moment obtained above, whence calculate the 
value of one inch of ordinate. Calculate the length corre- 
sponding to one degree on the surface of the paper drum, 
parallel to the ^T-axis. This will be the unit to be used in 
calculating the angle of torsion. Fix the paper on the drum 
and draw the datum-line or X-axis. Insert the test-piece be- 
tween the centres and screw in the centre until the neck of the 
test-piece is about midway between the jaws. Wedge the test- 
piece between the jaws as firmly as possible by hand, and then 
tap the wedges slightly with a copper hammer. Fasten an 
index-arm to each end of the specimen in such a manner that 
twisting or slipping of the specimen can be observed by ref- 
erence to the centre of the pendulum on one end, and to a 
fixed point on the drum on the opposite end. Throw the 
worm into gear and turn the handle slowly and steadily until 
rupture occurs, only relaxing the stress once or twice during 
the test. Take the record of all the test-pieces on the same 
sheet with the same origin of co-ordinates. 

Correct each diagram for amount of slipping of test-piece 
or yielding of frame by reference to index-arms carried by the 
test specimen. 

The record of torsion-tests, page 162, is a numerical example, 
obtained from diagrams similar to those shown in Fig. 98. 



IMPACT TESTS. 

105. Directions for Testing Cast-iron by Impact with 
Heisler's Impact Testing-machine. (See Article 76, p. 1 19.; 

Method. — Take a transverse test-bar of cast-iron and place 
it in the machine, cope side out, so that the blow will be 
struck in the middle of its length. Arrange the autographic 
device so that it will register the deflection of the bar. Place 
the tripping device or "dog" for a fall of two inches 
Catch the bob at this point, and trip at every notch above 



1 64 EXPERIMENTAL ENGINEERING. [§ I0& 

successively until the bar breaks. Note the maximum height 
of fall. Report on the experiment the behavior of the test- 
bar and character of its fracture, and the number of impacts 
and the force in inch-pounds of the last blow. Compute the 
resilience of the test-piece. Try a similar bar at same ultimate 
fall, and observe the number of blows required to break it. 
Draw conclusions. Write complete report, and give moduli 
and coefficients. 

106. Drop-tests. — The following method of making drop- 
tests has been recommended by the Committee on Standard 
Methods of Testing appointed by the American Society of 
Mechanical Engineers, and is substantially the same as adopted 
by the German Engineers at Munich in 1888 : 

Drop-tests are to be made on a standard drop », which is to 
embody the following essential points : 

a. Each drop-test apparatus must be standardized. 

b. The ball {falling mass) shall weigh 1000 or 1500 pounds; 
the smaller is, however, preferable. 

c. The ball may be made of cast-iron, cast or wrought 
steel ; the shape is to be such that its centre of gravity be as 
low as possible. 

d. The striking-block is to be made of forged steel, and is 
to be secured to the ball by dovetail and wedges in a rigid 
manner, and so that the striking-face is placed strictly sym- 
metrical about and normal to its vertical axis passing through 
the centre of gravity. Special permanent marks are to indi- 
cate the correctness of the face in these respects. 

Special marks should be made to indicate the centre of 
the anvil-block. 

e. The length of guides on the ball should be more than 
twice the width between the guides, which are to be made of 
metal ; i.e., rails so placed that the ball has but a minimum 
amount of play between them. Graphite is recommended as 
lubricant. 

f. The detachment or shears must not cause the ball to 
oscillate between the guides, and must be readily and freely 
controllable, with the point of suspension truly above the 



^ 



§ 10/.] TESTING MATERIALS OF CONSTRUCTION. 1 65 

centre of gravity of the ball ; and a short movable link, chain, 
or rope is to be fixed between the ball and shears or detach- 
ment. 

g. When a constant height of drop is used, an automatic 
detaching device is recommended. 

h. The bearings for the test-piece are to be rigidly attached 
to the scaffold or frame, and they should be, wherever possible, 
in one piece with it. 

i. The weight of frame, bearings, and anvil-block should be 
at least ten times that of the ball. 

k. The foundation should be inelastic, and consist of 
masonry, the magnitude of which is to be determined by the 
locality and subsoil. 

/. The surface struck should always be accurately level ; 
therefore proper shoes or bearing-blocks are to be provided 
for testing rails, axles, tires, springs, etc., etc., to insure a 
proper level upper surface ; these blocks are to be as light as 
possible. 

The exact shape of these bearing-blocks is to be given on 
each test report. 

m. The gallows or frame should be truly vertical and the 
guides accurately parallel. 

n. The height of fall of ball should be 20 feet clear, be- 
tween striking and struck surfaces. 

0. Drops which by friction of ball on guides absorb two 
per cent of the work due to impact are to be discarded. 

p. For large tests a ball weighing 2000 pounds is to be 
used. 

q. A sliding-scale is to be attached to the frame, and in 
such a manner that the zero-mark can always be placed on a 
level with the top of the test-piece. 

SPECIAL TESTS OF MATERIALS. 

107. The following comparative tests are often useful : 

1. The Welding-test. — This is to be done with a hammer 
weighing eight to ten pounds, with a given number of blows. 



1 66 EXPERIMENTAL ENGINEERING. [§ IO7. 

The weld is to be a simple scarf weld, made in a coke or gas 
flame without fluxes. Each bar to be tested to be treated in 
the same way, using in each case two or three samples of 
iron ; one sample to be tested on the tension-machine, the 
other to be nicked to the depth of the weld and then bent or 
broken, to show the character of the welded surfaces. 

2. The Bending-test. — This affords a ready means of find- 
ing the ductility of metals. The test-piece is to be bent about 
a stud having a diameter twice that of the specimen. The 
piece is to be bent with a lever, and no pounding is permitted. 
If the plate holding the stud is graduated, the angular deflec- 
tion at time of permanent set may be read at once. A modi- 
fication of the bending-test is often used to determine the 
property of toughness, by bending the specimen, first hot and 
then cold, until it is doubled over on itself. 

3. The Hardening-test is used in connection with the other 
tests to determine the qualities of the specimen ; the mate- 
rial, one specimen of which, having been previously welded, is 
carefully heated to a red heat, and plunged in water having a 
temperature of 32-40 degrees. This specimen is tested by 
torsion and bending, the same as the unhardened specimen. 

4. The Forging-test. — The material is brought to a red 
heat and hammered until cracks begin to show, the relative 
amount of flattening indicating the red-shortness of the ma- 
terial. Useful principally with rivet-rods. 

5. Punching-tests. — Find the least material that will stand 
between the edge and the hole punched, by measurement. 

6. Abrasion-tests. — Find the amount of wear from a given 
amount of work. 

7. Hammer-test. — This is made with a light hammer, and 
the character of the material is determined by the sound 
emitted. Is useful in locating defects in finished products* 
but of little value on test specimens. 

Fatigue of Metals, or the effect of repeated stresses, is a 
matter of great practical importance, and was investigated 
very extensively by Wohler. These results are discussed in 
full in a work by Weyrauch. It is well established that the 



'S 



.§ 108.] TESTING MATERIALS OF CONSTRUCTION. 1 67 

breaking-point is lowered by a large number of applications 
of stress. The proportional loads for wrought-iron, according 
to Wohler, being as follows : Breaking-load applied once, 4 ; 
tension alternating with no stress, 2 ; tension alternating with 
compression, 1. 

Rest of materials or removal of stress in some instances 
seems to restore both strength and elasticity. 

Viscosity or the fluidity of metals under certain conditions 
is also well established. 

The effect of temperature on the strength of metals has now 
been thoroughly investigated. The investigations at the 
Watertown Arsenal show that steel and wrought-iron bars in- 
crease slightly in tensile strength as the temperature increases 
to 6oo° F., and then decrease in proportion to increase of 
temperature, so that the breaking coefficients at 1600 F. lie 
between 10,000 and 20,000 pounds. See U. S. Report, Test 
of Metals, 1888. 

108. Tests required for Different Material.* — In general 
the material is to be tested in such a manner as to develop 
the same strains that will be called forth in the peculiar use to 
which it is devoted. 

The table, page 148, shows the tests that are prescribed for 
materials for various uses, by the Committee on Standard 
Tests and Methods of Testing of the American Society of 
Mechanical Engineers. 

Pipes and Pipe-fittings. — These should be subject to an 
internal hydraulic pressure. 

Car-wheels, — Car-wheels are usually subjected to the drop- 
test. The following method is employed by the Pennsylvania 
Railroad Company for testing cast-iron wheels : 

For each fifty wheels which have been shipped, or are 
ready to ship, one wheel is taken at random by the railroad 
company's inspector, either at the railroad company's shops or 
at the wheel-manufacturer's, as the case may be, and subjected 
to the following test: The wheel is placed flange downward 
on an anvil-block weighing 1700 pounds, set on rubble masonry 
two feet down, and having three supports not more than five 

* For detailed information see Proceedings Am. Soc. Testing Materials. 



1 68 



EXPERIMENTAL ENGINEERING. 

TABLE SHOWING TESTS REQUIRED. 
Required Test denoted by x. 



L§ 109. 



Material used for 


C 


'35 
c 
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H 


c 

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'35 

V 

a 
S 




i 

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rf 

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a 
a 

a 


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c 

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be 
a 

"c 
u 
•a 

u 
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c 
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u 




c 



'55 
re 

< 


i 

'■a 
a 


Railroad rails 


X 
X 
X 
X 
X 
X 
X 








X 
X 

X 


.... 


X 

X 










" car-axles . . . 
















" " tires 
















Shafting 


X 

X 
X 


X 
X 
X 
X 


X 














Building — wrought-iron .... 
" low steel. 




X 


X 
X 
X 














X 

X 








" high steel 

Boiler — wrought-iron 


























" plates. 


X 
X 
X 
X 




X 








X 
X 
X 
X 


X 


X 
X 
X 
X 






" shape-iron 






X 




" rivet-rods 












" low steels 














Ship materials 














" plates 


X 
X 
X 
X 
X 
X 
X 












X 
X 
X* 






















:. 


X 






Wire 






















A 








X 
X 
X 
X 








X 
X 










Copper and soft metals 

Woods. 


















X 

X 



















































* Repeat in both directions— also by winding. t Longitudinal. 

inches wide for the wheel to rest upon. This arrangement 
being effected, the wheel is struck centrally on the hub by a 
weight of 140 pounds, falling from a height of twelve feet. 
Should the wheel break in two or more pieces before nine 
blows or less, the fifty wheels represented by it are rejected. 
If the wheel stands eight blows without breaking in two or 
more pieces, the fifty wheels are accepted. 

109. Methods of Testing Bridge-materials. — The follow- 
ing directions are abstracted from the standard specifications 
adopted by bridge-builders.* 

Wrought-iron. 1. Appearance. — All wrought-iron must be 
tough, ductile, fibrous, and of uniform quality for each class ; 



* See Handbook published by Carnegie, Phipps & Co., Pittsburg. 



§ IO9.] TESTING MATERIALS OF CONSTRUCTION. 



169 



straight, smooth, free from cinder pockets or injurious flaws, 
buckles, blisters, or cracks. When rolls are working at maxi- 
mum thickness, poorer finish will be accepted. 

2. Manufacture. — No special process of manufacture re- 
quired. 

3. Standard Test-piece. — The tensile strength, limit of elas- 
ticity and ductility shall be determined from a standard test- 
piece, not less than one quarter-inch in thickness, cut from a 
full-sized bar, and planed or turned parallel ; if the cross-sec- 
tion is reduced, the tangent between shoulders shall be at 
least twelve times its shortest dimensions, and the minimum 
area of cross-section shall not be less than one fourth square 
inch in area and not more than one square inch. Whenever 
practicable, two opposite sides of the piece are to be left as 
they come from the rolls. A full-sized bar if less than the re- 
quired dimensions may be used as its own test-piece. 

The ductility, or per cent of strain, is obtained by measuring 
the elongation after breaking from the point of rupture both 
ways, on an original length, ten times the least cross-section, 
or at least five inches long. 

In this length must occur the curve of reduction of area. 

4. Strength. — The strength of the specimens to be a func- 
tion of the size, and to be determined by the formulae in the 
following table : 

STRENGTH OF IRON REQUIRED FOR BRIDGE-BUILDING. 



Character of the Iron. 



Tension-iron, pins and bolts, and ) 

plate-iron less than 8 inches wide, f 

Plate-iron 8 to 24 inches wide 

24 to 36 " " 

36 to 48 " " 

Shaped iron not specified above : 

" less than £ inch thick 

" over ■£ inch thick 



Formulae for Ulti- 
mate Strength. 
Pounds per sq. in. 
T 



joooA 
52000 — 

48000 



46000 



50000 — 



yoooA 



Strength at 

Elastic Limit. 

Per cent of 

Breaking. 



5° 
54-2 
5i-5 



50 



Elongation 

at Rupture. 

Per cent. 



20 

12 
IO 

5 



170 EXPERIMENTAL ENGINEERING. [§ IO9. 

In above formulae A represents area in square inches, B 
circumference in inches. 

5. Hot-bending. — All plates and angles must stand at a 
working heat a sharp bend at right angles without sign of 
fracture. 

6. Rivet-iron. — Rivet-iron must be tough and soft, and 
capable of bending cold until the sides are in close contact. 

7. Cold-bending. — All tension-iron pins, bolts, and plate 
less than 8 inches wide, must bend cold 180 , to a curve whose 
inner radius equals the thickness, without sign of fracture. 

8. Specimens of full thickness, from plate-iron or from 
flanges or webs of shaped iron, must bend cold through 90 to 
a curve whose inner radius is \\ times its thickness. 

9. Number of Test-pieces. — Four standard test-pieces to be 
tested free of cost on each contract, with one additional for 
each 50,000 pounds of iron, and as many more as the con- 
tractor will pay for at $5 each. If any test-piece gives results 
more than 4 per cent below the requirements, the particular 
bar from which it was taken may be rejected, but the results 
shall be included in the average. If any test-piece have a 
manifest flaw, its test shall not be considered. Two test-bars 
out of ten falling more than 4 per cent below the requirements 
shall be a cause for rejecting the whole lot from which they 
were taken as a sample. 

A variation of more than 2\ per cent of weight will also be 
a cause for rejection. 

Steel. — The requirements as for manufacture, finish, num- 
ber of test-pieces and method of testing as for iron. 

1. Test-pieces. — Round test-pieces are to be obtained from 
three separate ingots of each cast, not less than three quarters 
of an inch in diameter and of a length not less than eight 
inches between the jaws of the testing-machine. These bars 
are to be truly rounded, finished at a uniform heat, and ar- 
ranged to cool uniformly, and from these test-pieces alone the 
quality of the material shall be determined. 

2. Strength. — All the above-described bars are to have a 
tensile strength, not less than 4000 pounds of that specified, an 



§ I09-] TESTING MATERIALS OF CONSTRUCTION. \J \ 

elastic limit not less than one half the tensile strength of the 
test-bar, a percentage of elongation not less than 1,200,000, 
divided by the tensile strength in pounds per square inch ; and 
a percentage of reduction of area not less than 2,400,000 di- 
vided by the tensile strength in pounds per square inch. The 
elongation should be measured after breaking on a specimen, 
with length at least ten times the least diameter of the cross- 
section, in which length must occur the entire curve of reduc- 
tion from stretch. 

Directions for testing and rejecting specimens same as for 
iron. 

3. Rivet-steel. — The required strength is 60,000 pounds 
tensile strength, with elastic limit, elongation, and fracture as 
in clause 2. To be rejected if under 56,000 pounds, and to 
stand the same bending-test as rivet-iron. 

Cast-iron. — All castings, except where chilled iron is 
specified, shall be tough gray iron, free from cold-shuts or 
blow-holes, true to pattern and of workmanlike finish. Sample 
pieces I inch square, cast from the same heat of metal in sand- 
moulds, shall sustain on a clear space of 4 feet 6 inches a cen- 
tral load of 500 pounds. 

Workmanship. — Workmanship must be first-class ; fin- 
ished surfaces protected by white-lead and tallow ; rivet- 
holes accurately spaced, and truly opposite before the rivets 
are driven. 

Rivets must completely fill the holes, and be of a height 
not less than 0.6 diameter of the rivet. 

Eye-bars and Pin-holes. — Pin-holes must be accurately 
bored, and within -^ inch of position shown on drawing; its 
diameter not to exceed that of the pin by 0.02 inch if under 3J- 
inches, or by 0.03 inch if over 3-^ inches. 

Eye-bars must be straight, with holes in centre-line and in 
centre of head, and no welds in the body of the bar. All 
chord eye-bars from the same panel must permit pins to be 
easily inserted when placed in a pile. 

Tests of Eye-bars. — Tests are to be made on full-size 



I7 2 EXPERIMENTAL ENGINEERING. \% I IO. 

specimens, rolled at the same time as those required for the 
structure. 

The lot to which the sample test-bars belong shall be ac- 
cepted when — 

a. Not more than one third the bars tested, break in the 
eye. 

b. Or if more than one third break in the eye, the ten- 
sile strength is within 5 per cent required by the formula, 

iqoqA 
T= 52000 — — 75 — — 500 (width of bar) ; all in inches. 

Steel bars must show a strength within 4000 pounds of 
that required in clause 13. 

A variation in thickness of heads will be allowed, not ex- 
ceeding -g^ inch small, or ^ inch large, from the specifications. 

Annealing. — If a steel piece is partially heated during the 
progress of the work, the whole piece must be subsequently 
annealed. All bends in steel must be made cold, or the piece 
must be subsequently annealed. 

1 10. Admiralty Tests. 

Tests for Iron Plate. 

Hot, to bend without fracture from 90 to 125 . 

Cold, to bend without fracture to the following angles : 
I -inch plate., .lengthwise io° to 15 , crosswise 5 
f- " " ... " 20°t0 25°, " 5 to 10° 

• i- " " ... " 30° to 35 , " io° to 15 
J- " "... " 55°to7o°, " 20 to 30* 

Tests for Plate Steel.* 

I. Strength. — Strips cut lengthwise or crosswise of the plate 
to have an ultimate tensile strength of not less than 26 and 
not exceeding 30 tons per square inch of section, with an 
elongation of 20 per cent in a length of 8 inches. 

* See " Manual of the Steam-engine," Vol. II., page 488, by R. H. Thurston. 



§ III.] TESTING MATERIALS OF CONSTRUCTION. 1 73 

2. Temper. — Strips cut lengthwise of the plate if inches 
wide, heated uniformly to a low cherry-red and cooled in 
water of 82 F., must stand bending in a press to a curve of 
which the inner radius is one and a half times the thickness of 
the plates tested. 

3. The strips are to be cut in a planing-machine, and have 
sharp edges removed. 

4. The ductility of every plate is to be tested by the appli- 
cation of the shearing or bending tests on the contractor's 
premises and at his expense. The plates are to be bent cold 
with the hammer. 

5. All plates to be free from lamination and injurious 
surface defects. 

6. One plate out of every fifty or fraction thereof to be 
taken for testing by tensile and tempering test from every 
invoice. 

7. The pieces cut out for testing are to be of parallel width 
from end to end, or for at least 8 inches in length. A latitude 
or variation in thickness will be permitted of 10 per cent for 
plates less than one half-inch thick, and of 5 per cent for plates 
over that thickness. 

Tests for Angle, Bulb, or Bar Steel. 

1, 2. Strength and Temper. — The requirements the same as 
for plate steel. 

3. Number of Tests. — Cross ends to be cut off, and one 
piece for each fifty or fraction thereof to be tested in each 
invoice. 

in. Lloyd's Tests for Steel used in Ship-building.* 
I. Strength. — Strips cut lengthwise or crosswise of the plate, 
and also angle and bulb steel, to have an ultimate tensile 
strength of not less than 27 and not exceeding 31 tons per 
square inch of section, with an elongation corresponding to 20 
per cent on a length of 8 inches before fracture. 

2. Temper. — Tempering test the same as the Admiralty 

*See Thurston's " Steam-engine," Vol. II. 



174 EXPERIMENTAL ENGINEERING. [§ II 3. 

test, except that inner radius of bend is three times the 
thickness. 

Rivets to be same size as required for iron. 

112. Standard Specifications for Cast-iron Water-pipe, 

Adopted by the American Water-works Association, Phila- 
delphia, 1 891. (Abstract from Transactions.) 

1. Length. — Each pipe shall be of the kind known as 
"socket and spigot," and shall be 12 feet long from bottom 
of the socket to the end of the pipe. 

2-7. Metal. — The metal shall be best quality neutral pig- 
iron, with no admixture of cinder, cast in dry-sand moulds, 
placed vertically, numbered and marked with name of maker 
and date of making. The shell to be smooth and round, with- 
out imperfections, and of uniform thickness. 

8-10. Test-bars. — Test-bars to be 26 inches long, 2 inches 
wide, and I inch thick, and to be tested for transverse strength. 
These bars shall stand, when carried flatwise on supports 24 
inches apart, a centre load of 1900 lbs., and show a deflection 
of not less than 0.25 inch before breaking. Test-bars are to 
be cast when required by the inspector, and to bd as nearly as 
possible the specified dimensions. 

12-16. All pipes to be thoroughly cooled when taken from 
the pit, afterward thoroughly cleaned without the use of acid, 
then heated to 300 F., and plunged into coal-pitch varnish. 
When removed, the coating to fume freely and set hard within 
an hour* 

17. Testing. — The pipes to be tested after the varnish hard* 
ens with hydrostatic pressure of 300 lbs. per square inch for all 
sizes below 12 inches diameter, and 250 lbs. for all above that 
diameter, and simultaneously to be struck with a 3-lb. hammer. 

18-20. Templates to be furnished by the maker ; the weight 
of pipe to vary not over 3 per cent from the standard ; all tests 
to be made at expense of maker. 

113. Tests of Stone, Brick, Cements. — These materials 
are principally used in walls of buildings and for foundations. 
For this use they are subjected principally to compression 



§ U4-] TESTING MATERIALS OF CONSTRUCTION. 17 5 

or crushing stresses. The important properties are strength 
and durability. Stone is usually tested for compressive and 
transverse strength, brick for compressive strength, and cement 
and mortar for tension. 

114. Testing Stones. — The specimens for compressive 
strength are cubes of various sizes, depending principally on 
the capacity of the testing-machine. These cubes are to be 
nicely made with the opposite sides perfectly parallel to pro- 
vide a uniform bearing-surface. It is found that the larger 
the blocks the greater the strength per unit of area.* 

To test Stone for Compressive Strength. — Have the specimen 
dry and dressed, and ground to a cube — inches on each 
edge, and with the opposite faces parallel planes. This is 
important, as imperfect or wedge-shaped faces concentrate the 
stress on a small area. In testing, use a layer of wet plaster-of- 
Paris between the specimen and the faces of the machine, to 
distribute the stress. 

To test Stone for Transverse Strength. — In this case the 
specimen is dressed into the form of a prism 8 inches long 
and 2 by 2 inches in section. It is supported on bearings 6 
inches apart, and a centre load applied. The strength is 
computed as explained under head of Transverse Testing, 
page 78. 

Durability of stone is tested accurately only by actual trial. 
Some idea can be formed by noticing the effect of the weather 
on the exposed rocks in the quarry from which the specimen 
came. 

In the method of standard tests adopted in Munich in 1887 
the following additional tests are recommended: 

I. Trial method with (a) a jumper or drill, (b) by rotary 
boring. The amount of work done by the drill to be deter- 
mined by the momentum of drop, its velocity of rotation, and 
the shape or cutting angle of the drill or cutting tool. These 
qualities are to be determined by comparison with a standard 



* See Unwin, "Testing of Materials. 



1 76 EXPERIMENTAL ENGINEERING. [§ II4, 

drill working under definite conditions. 2. Examine the stone 
for resistance to shearing as well as to boring. 

Report the results of the boring test on the following form : 

STANDARD REPORT BLANK FOR BORING TEST. 

1. Description of stone in its geological and mineralogical relations. 

2. Miner's classification (hard, very hard, or extremely hard). 

3. Texture \\. e., coarse-grained, fine-grained, parallel, normal to or inclined 
to axis of drill-hole). 

4. Specific gravity of the stone. 

5. Diameter of hole drilled. 

6. Diameter of hole and core when boring. 

7. Straight or curve edged drills. 

8. Angle of edge of drills. 

0. Number of blows per revolution of drill. 

10. Effective weight of drill. 

11. Mean effective drop of drill. 

12. Number of blows required to drill the depth of hole. 

13. Number and form of teeth of borer. 

14. Statement of pressure on and velocity of bore, while boring. 

15. Actual or total depth of bore-hole. 

16. Calculated or indicated work done during boring stated in meter-kilo- 
grams per c. m. of hole bored. (When using a hollow borer the annulus ot 
stone cut away is alone to be considered.) 

3. Find when possible the position in the quarry originally 
occupied by the specimen tested. 

4. Find out the intended use of the stone, and determine 
the character of tests largely from that. 5. Dry the stone 
until no further loss of weight occurs at a temperature of 30 C. 
(86° F.), and test in a dry condition. 

Make the tests for strength as described, using as large 
specimens as possible. Also, test by compression rectangular 
blocks. Test also for tension and bending. 

6. Obtain the specific gravity, after drying at a temperature 
of 86° F. 

7. Examine the specimen for resistance to frost by using 
samples of uniform size, 7 cm. (2.76 inches) on each edge. 

8. The frost-test consists of : 

a. The determination of the compressive strength of satti* 
rated stones, and its comparison with that of dried pieces. 



§ 1 1 4-] TESTING MATERIALS OF CONSTRUCTION. I 77 

b. The determination of compressive strength of the dried 
stone after having been frozen and thawed out twenty-five 
times, and its comparison with that of dried pieces not so 
treated. 

c. The determination of . the loss of weight of the stone 
after the twenty-fifth frost and thaw. Special attention must 
be had to the loss of those particles which are detached by the 
mechanical action, and also those lost by solution in a definite 
quantity of water. 

d. The examination of the frozen stone by use of a magni- 
fying-glass, to determine particularly whether fissures or scal- 
ing occurred. 

9. For the frost-test are to be used : 

Six pieces for compression-tests in dry condition, three 
normal and three parallel to the bed of the stone, provided 
these tests have not already been made, in which it is permis- 
sible, on account of the law of proportions, to use cubical test- 
blocks larger than 7 cm. (2.76 inches). 

Six test-pieces in saturated condition — not frozen, how- 
ever ; three tested normal to and three parallel to bed. 

Six test-pieces for tests when frozen, three of which are to 
be tested normal to and three parallel to bed of stone. 

10. When making the freezing-test the following details are 
to be observed : 

a. During the absorption of water the cubes are at first to 
be immersed but 2 cm. (0.77 inch) deep, and are to be lowered 
little by little until finally submerged. 

b. For immersion, distilled water is to be used at a tem- 
perature of from 1 5 C. (59 F.) to 20 C. (68° F.). 

c. The saturated blocks are to be subjected to temperatures 
of from — io° to — 15 C. (14 to 5 F.). This can be done in 
a vessel surrounded with melting ice and salt. 

d. The blocks are to be subjected to the influence of such 
cold for four hours, and they are to be thus treated when 
completely saturated. 

e. The blocks are to be thawed out in a given quantity of 
distilled water at from 59 F. to 64 F. 



I7 8 EXPERIMENTAL ENGINEERING. IS 1 * 5- 

II. An investigation of zveathering qualities — stability un- 
der influences of atmospheric changes — can be neglected when 
the frost-test has been made. However, the effects in this re- 
spect, in nature, are to be carefully observed and compared with 
previous experience in the use of similar material. Observe — 

a. The effect of the sun in producing cracks and ruptures 
in stones. 

b. The effect of the air, and whether carbonic-acid gas is 
given off. 

c. The effect of rain and moisture. 

d. The effect of temperature. 

115. Bricks or Artificial Building-stone.— Brick are tested 
for strength, principally by compression. 

1. They should be ground to a form with opposite parallel 
faces, and are tested between layers of thin paper; or, without 
grinding, between thin layers of plaster-of-Paris, as explained for 
stone. The variation in size of specimen, and whether the brick 
is tested on end, side-ways, or flat-ways, will make a great differ- 
ence in the results. The test, to be of any value, must state 
the method of testing. Whole bricks are stronger per unit of 
area than portions of bricks, and should be used when practi- 
cable. 

2. It is also recommended that brick be tested for compres- 
sion in the shape of two half-bricks superimposed, united by a 
thin layer of Portland cement, and covered on top and bottom 
with a thin layer of such paste to secure even bearing- 
surfaces.* 

3. The transverse test for brick is believed to be a valuable 
index to its building properties. Support the brick on knife- 
edges 6 inches apart, and apply the load at the centre. Com- 
pute the modulus of rupture : 

K ~~2 bd" 






*See Vol. XI. (Standard Method of Testing), Transactions of American 
Society Mechanical Engineers, regarding Articles 114-118. 



§ 1 1 6.] TESTING MATERIALS OF CONSTRUCTION. \Jg 

in which W equals the centre-load, / the length, b the breadth, 
d the depth, all in inches. 

4. Dry as for stone, and determine the specific gravity. 

5. Test hard-burned and soft-burned from the same kiln. 

6. Determine the porosity of the brick as follows : 
Thoroughly dry ten pieces on an iron plate ; weigh these 

pieces ; then submerge in water to one half the depth for 
twenty-four hours ; then completely submerge for twenty-four 
hours, dry superficially, and weigh. Determine porosity from 
the weight of water absorbed, which should be expressed as 
per cent of volume. Express absorption as per cent of weight. 

7. Determine resistance against frost, as previously ex- 
plained for stones, using five specimens, and repeating the 
operation of freezing and thawing twenty-five times for each 
specimen. Observe the effect with a magnifying-glass. After 
freezing, test for compression, and compare the results with 
that obtained with a dry brick. 

8. To test brick for soluble salts, obtain samples from an 
underburned brick and grind these to dust. Sift through a 
sieve 4900 meshes per square cm. (31,360 per square inch). 
The dust sifted out is lixiviated in 250 c.c. of distilled water, 
boiled for about one hour, filtered, and washed. The amount 
of soluble salts is then determined by boiling down the solu- 
tion and bringing the residue to a red heat for a short time. 
The amount is determined by weight and expressed in per- 
centage ; its composition is determined by a chemical analysis. 

9. Determinations of the presence of carbonate of lime, 
mica, or pyrites are to be made by chemical analysis. 

116. Tests of Paving Material, Stones, and Ballast, 
Natural and Artificial. — In this case the following observa- 
tions and tests should be made : 

1. Information in regard to petrographic and geologic 
classification, the origin of the samples, etc., etc. ; also : 

2. Statement in regard to utilization of same. 

3. Specific gravity of the samples is to be determined. 

4. All materials used in the construction of roads, provided 
they are not to be used under cover or in localities without 



l8o EXPERIMENTAL ENGINEERING. [§ 1 16. 

frost, are to be tested for their frost-resisting qualities by similar 
test to those prescribed for natural stone. 

5. Stones or brick used for paving are tested most satisfac- 
torily in a manner representing their mode of utilization by de- 
termining the wearing qualities by an abrasion-test described 
by Prof. I. 0. Baker as follows :* The abrasion-tests are made 
by putting the bricks and a number of pieces of iron into a re- 
volving horizontal cylinder. The cylinder used by Prof. Baker 
was a foundry-rattler 45 inches long, 26 inches in diameter, and 
revolved at rate of 24 revolutions per minute. The iron used 
consisted of 546 pieces of " foundry-shot," weighing about J- 
pound each, thus making a total weight of 83J pounds. 

In making the test, the " brick " is inserted in the rattler, 
which is put in motion and the loss determined by weighing 
at the end of each run. Three runs are made, each one half- 
hour in length ; the comparisons are all made from the loss 
during the third run, expressed in percentages. Granite and 
various stones treated in the same way afford a valuable basis 
for comparison. 

The uniformity of wearing qualities of brick for parts more 
or less distant from the exterior surface is determined by re- 
peating the trial on the same piece, and not merely testing one, 
but a greater number of pieces. It is, moreover, necessary to 
test samples of the best, the poorest, and the medium qualities 
of bricks in any one kiln. 

6. Obtain the transverse strength as explained. 

7. Obtain the per cent of water absorbed after the bricks 
have been thoroughly dried at 30 C. (83 F.), as explained 
Arts. 91-95. 

8. Test materials for ballast in a similar manner. 

9. In some cases it may be desirable to test stones as to the 
capacity for receiving a polish. 

10. Examinations of asphalts can only be made in an 
exhaustive manner by the construction of trial roads. An 



See Clay-worker t August and September 1891. 



§ 1 1 70 TESTING MATERIALS OF CONSTRUCTION. l8l 

opinion coinciding with the results of such trial may be formed 
by- 

(a) Determination of the quantity and quality of the bitu- 
men contained therein (whether the bitumen be artificial or 
natural). 

{b) By physical and chemical determination of the residue, 

(c) By determination of the specific density of test-pieces of 
the material used by a needle of a circular sectional area of I 
sq. mm., carrying a weight of 300 grams. (See Art. 1 18, p. 163.) 

(d) By the determination of the wear of such test-pieces by 
abrasion or grinding trials. 

(e) By the determination of the resistance to frost of these 
test-pieces. (See Art. 119, page 163.) 

117. Hydraulic Cements and Mortars — Definitions.— 
The standard scientific methods of testing cements depend prin- 
cipally upon researches conducted in the German laboratories. 
The standard method as here given is that recommended by 
the Committee on Standard Methods of Testing at Munich in 
1888. 

The following definitions will serve to distinguish the dif- 
ferent classes of hydraulic bond materials : 

1. Common limes are produced by roasting or burning lime- 
stones containing more or less clay or silicic acid, and which 
when moistened with water become wholly or partly pulverized 
and slaked. According to local circumstances, these are sold 
in shape of lumps or in a hydrated condition in the shape of a 
fine flour. 

2. Water-limes and Roman cements are products obtained by 
burning clayey lime marls below the temperature of decrepita- 
tion, and which do not disintegrate upon being moistened, but 
must be powdered by mechanical means. 

3. Portland cements are products obtained by burning clayey 
marls or artificial mixtures of materials containing clay and lime 
at decrepitation temperature, and are then reduced to the fine- 
ness of flour, and which contain for one part of hydraulic 
material at least 1.7 parts of calcareous earth. To regulate 



1 82 EXPERIMENTAL ENGINEERING, [§ 1 1 8. 

properties technically important, an admixture of 2 per cent 
of foreign matter is admissible. 

4. Hydraulic fluxes are natural or artificial materials which 
in general do not harden of themselves, but do so in presence 
of caustic lime, and then in the same way as a hydraulic ma= 
terial ; i.e., puzzuolana, santorine earth, trass produced from a 
proper kind of volcanic tufa, blast-furnace slag, burnt clay, 

5. Puzzuolana cements are products obtained by most care 
fully mixing hydrates of lime, pulverized, with hydraulic fluxes 
in the condition of dust. 

6. Mixed cements are products obtained by most carefully 
mixing existing cements with proper fluxes. Such bond ma- 
terials are to be particularly stated as " Mixed Cements," zt 
the same time naming the base and the flux used. 

Mortar is made by mixing three or four parts of sharp sand 
with one part of quick-lime or cement, and adding water until 
of tfie proper consistency. Mortar made from quick-lime will 
neither set nor stay hard underwater; that made from hydraulic- 
or water-lime, if allowed to set in the air, will not be softened 
by water; while that made from cement will harden under 
water. 

118. Method of Testing Cements. — The principal prop- 
erties which are necessary to know are : (1) its fineness; (2) time 
of setting ; (3) its tensile strength ; (4) its soundness or freedom 
from cracks after setting ; (5) its heaviness or specific gravity ; 
(6) its crushing strength ; (7) its toughness or power to resist defi- 
nite blows. 

The following standard method of testing cements was adopted 
by a committee ot the American Society of Civil Engineers and 
of the American Society of Testing Materials in 1903 and 1904. 

Selection 0) Sample— -The sample shall be a fair average of 
the contents of the package; it shall be passed through a sieve 
having 20 meshes per lineal inch before testing to remove lumps. 
In obtaining a sample from barrels or bags, an auger or sampling- 
iron reaching to the centre should be used. 

A chemical analysis, if required, should be made in accord- 



§ II 8.] TESTING MATERIALS OF CONSTRUCTION. 



183 



ance with the directions in the Journal of the Society of Chemical 
Industry, published Jan. 15, 1902. 

Specific Gravity. — This is most conveniently made with Le 
Chatelier's apparatus, which consists of a flask (D) 7 Fig. 99, of 




'Pig. 99. — Le Chatelier's Specific-gravity Apparatus. 



120 cu. cm. (7.32 cubic inches) capacity, the neck of which is about 
20 cm. (7.87 inches) long; in the middle of this neck is a bulb 
(C), above and below which are two marks (F and E); the 
volume between these marks is 20 cu. cm. (1.22 cubic inches). The 
neck has a diameter of about 9 mm. (0.35 in.), and is gradu- 
ated into tenths of cubic centimeters above the mark F. Ben- 
zine (62 ° Baume naphtha), or kerosene free from water, should 
be used in making the determination. 

The specific gravity can be determined in two ways: (1) The 
flask is filled with either of these liquids to the lower mark (E), 
and 64 gr. (2.25 ounces) of powder, previously dried at ioo° C. 
(2 1 2 F.) and cooled to the temperature of the liquid, is grad- 
ually introduced through the funnel (B) [the stem of which ex- 
tends into the flask to the top of the bulb (C)], until the upper 
mark (F) is reached. The difference in weight between the 
cement remaining and the original quantity (64 gr.) is the weight 
which has displaced 20 cu. cm. 



1 84 EXPERIMENTAL ENGINEERING. [§ I 1 8. 

(2) The whole quantity of the powder is introduced, and the 

level of the liquid rises to some division of the graduated neck. 

This reading plus 20 cu. cm. is the volume displaced by 64 gr. of 

the powder. The specific gravity is then obtained from the 

formula : 

_ . Weight of cement 

Specific gravity = ^ — \ : : . 

J Displaced volume 

The flask during the operation is kept immersed in water in 
a jar, A, in order to avoid variations in the temperature of the 
liquid. Different trials should agree within 1 per cent. 

The apparatus is conveniently cleaned by inverting the flask 
over a glass jar, then shaking it vertically until the liquid starts 
to flow freely. Repeat this operation several times. 

Fineness. — The fineness is determined by the use of circular 
sieves, about 20 cm. (7.87 inches) in diameter, 6 cm. (236 inches) 
high, and provided with a pan 5 cm. (1.97 inches deep, and a 
cover. 

The wire cloth should be woven (not twilled) from brass wire 
having the following diameters: 

No. 100, 0.0045 inch; No. 200, 0.0024 inch. 

This cloth should be mounted on the frames without distor- 
tion; the mesh should be regular in spacing and be within the 
following limits: 

No. 100, 96 to 100 meshes to the linear inch; 
No. 200, 188 to 200 " " " " 

50 to 100 gr. dried at a temperature of 212 F. prior to sieving 
should be used for the test, the sieves having previously been 
dried. 

The coarsely screened sample is weighed and placed on the 
No. 200 sieve, which is moved forward and backward, at the 
same time striking the side gently with the palm of the other 
hand, at the rate of about 200 strokes per minute. The opera- 
tion is continued until not more than one tenth of one per cent 
passes through per minute. The work is expedited by placing 



§ 1 1 8.] TESTING MATERIALS OF CONSTRUCTION, 1 85 

in the sieve a small quantity of large shot, or, better, some flat 
pieces of brass or copper about the size of a cent. The residue 
is weighed, then placed on a No. 100 sieve and the operation 
repeated. The results should be reported to the nearest tenth 
of one per cent. 

Normal Consistency. — The use of a proper percentage of 
water in mixing the cement or mortar is exceedingly important. 
No method is entirely satisfactory, but the following, which con- 
sists in the determination of the depth of penetration of a wire 
of a known diameter carrying a specified weight, is recommended 
The apparatus recommended is the Vicat needle shown in Fig. 
100, which is also used for determining the time of setting. This 
consists of a frame, K, bearing a movable rod, L, with a cap, 
D, at one end, and at the other the cylinder, G, 1 cm. (0.39 inches) 
in diameter, the cap, rod, and cylinder weighing 300 gr. (10.58 
oz.). The rod, which can be held in any desired position by a 
screw, F, carries an indicator, which moves over a graduated 
scale attached to the frame, K. The paste is held by a conical 
hard- rubber ring, 7, 7 cm. (2.76 inches) in diameter at the base, 
4 cm. (1.57 inches) high, resting on a glass plate, /, about 10 cm. 
(3.94 inches) square. 

In making the determination, the same quantity of cement 
as will be subsequently used for each batch in making the 
briquettes (but not less than 500 grams) is kneaded into a paste 
and quickly formed into a ball with the hands, completing the 
operation by tossing it six times from one hand to the other, 
maintained 6 inches apart ; the ball is then pressed into the rubber 
ring, through the larger opening, smoothed off, and placed (on 
its large end) on a glass plate and the smaller end smoothed 
off with a trowel; the paste, confined in the ring, resting on the 
plate, is placed under the rod bearing the cylinder, which is 
brought in contact with the surface and quickly released. 

The paste is of normal consistency when the cylinder pene- 
trates to a point in the mass 10 mm. (0.39 inch) below the top 
of the ring. Great care must be taken to fill the ring exactly 
to the top. 



1 86 



EXPERIMENTAL ENGINEERING. 



[§n8. 



The trial pastes are made with varying percentages of water 
until the correct consistency is obtained. 

The Committee has recommended, as normal, a paste the 
consistency of which is rather wet, because it believes that varia- 
tions in the amount of compression to which the briquette is 
subjected in moulding are likely to be less with such a paste. 





ML W sl 

' iff I, Jw 



Fig. ioo. — Vicat Needle. 



Time of Setting. — The object of this test is to determine the 
time which elapses until the paste ceases to be fluid and plastic, 
called the initial set, and also the time required for it to acquire 
a certain degree of hardness, called the final set. 

For this purpose the Vicat needle, which has already been 
described, should be used. In making the test, a paste of normal 
consistency is moulded and placed under the rod (X), Fig. ioo; 
this rod when bearing the cap (D) weighs 300 gr. (10.58 oz.). 
The needle (H), at the lower end, is 1 mm. (0.039 inch) in 



§ H9-] TESTING MATERIALS OF CONSTRUCTION. 1 8/ 

diameter. Then the needle is carefully brought in contact with 
the surface of the paste and quickly released. 

The setting is said to have commenced when the needle ceases 
to pass a point 5 mm. (0.20 inch) above the upper surface of the 
glass plate, and is said to have terminated the moment the needle 
does not sink visibly into the mass. 

The test-pieces should be stored in moist air during the test. 
This is accomplished by placing them in a rack over water con- 
tained in a pan and covered with a damp cloth, the cloth to be 
kept away from them by means of a wire screen, or preferably 
they may be stored in a moist box or closet. 

The determination of the time of setting is only approxi- 
mate, since it is materially affected by the temperature of the 
mixing water, the percentage of the water used, and the amount 
of moulding the paste receives. 

Standard Sand. — The committee recommend at present the 
use of a natural sand from Ottawa, 111., screened to pass a sieve 
having 20 meshes per lineal inch and retained on a sieve having 
30 meshes per lineal inch; the wires to have diameters of 0.0165 
and 0.0112 inch respectively. This sand will be furnished by 
the Sandusky Portland Cement Co., Sandusky, Ohio, at a mod- 
erate price. This sand gives in testing considerably more strength 
than the crushed quartz of the same size formerly employed 
for this purpose. 

Form of Briquette. — The form of briquette recommended is 
shown in Fig. 94. It is substantially like that formerly used 
except that the corners are rounded. 

Moulds. — The moulds should be made of brass, bronze, or 
some equally non-corrodible material, and gang moulds of the 
form shown in Fig. 92 are recommended. They should be 
wiped with an oily cloth before using. 

119. Mixing. — All proportion^ should be stated by weight; 
the quantity of water to be used should be stated as a percentage 
of the dry material. The metric system is recommended be- 
cause of the convenient relation of the gram and the cubic centi- 
meter. The temperature of the room and the mixing water 



1 88 EXPERIMENTAL ENGINEERING. [§ 1 1 9. 

should be as near 21 C. (70 F.) as it is practicable to main- 
tain it. 

The sand and cement should be thoroughly mixed dry. The 
mixing should be done on some non-absorbing surface, preferably 
plate glass. If the mixing must be done on an absorbing surface, 
it should be thoroughly dampened prior to use. The quantity 
of material to be mixed at one time depends on the number of 
test-pieces to be made; about 1000 gr. (35.28 oz.) makes a con- 
venient quantity to mix, especially by hand methods. 

The material is weighed, dampened, and roughly mixed with 
a trowel, after which the operation is completed by vigorously 
kneading with the hand for \\ minutes. 

Moulding. — Having worked the mortar to the proper con- 
sistency it is at once placed in the mould by hand, being pressed 
in firmly with the fingers and smoothed off with a trowel without 
ramming, but in such a manner as to exert a moderate pressure. 
The mould should be turned over and the operation repeated. 
The briquettes should be weighed prior to immersion, and those 
which vary in weight more than 3 per cent from the average 
should be rejected. 

Storage of the Test-pieces. — During the first twenty-four hours 
after moulding, the test-pieces should be kept in moist air to 
prevent them from drying out. A moist closet or chamber is so 
easily devised that the use of the damp cloth should be abandoned 
if possible. Covering the test-pieces with a damp cloth is ob- 
jectionable, as commonly used, because the cloth may dry out 
unequally, and, in consequence, the test- pieces are not all main- 
tained under the same condition. Where a moist closet is not 
available, a cloth may be used and kept uniformly wet by im- 
mersing the ends in water. It should be kept from direct con- 
tact with the test-pieces by means of a wire screen or some similar 
arrangement. 

A moist closet consists of a soapstone or slate box, or a metal- 
lined wooden box — the metal lining being covered with felt and 
this felt kept wet. The bottom of the box is so constructed as 
to hold water, and the sides are provided with cleats for holding 



§ I 1 9-] TESTING MATERIALS OF CONSTRUCTION. 189 

glass shelves on which to place the briquettes. Care should be 
taken to keep the air in the closet uniformly moist. 

After twenty-four hours in moist air the test-pieces for longer 
periods of time should be immersed in water maintained as near 
21 C. (70 F.) as practicable; they may be stored in tanks or 
pans, which should be of non-corrodible material. 

Tensile Strength. — The tests may be made on any standard 
machine. A solid metal clip, as shown in Fig. 93, is recommended. 
This clip is to be used without cushioning at the points of con- 
tact with the test specimen. The bearing at each point of con- 
tact should be J inch wide, and the distance between the centre 
of contact on the same clip should be ij inches. 

Test-pieces should be broken as soon as they are removed 
from the water, the load being applied uniformly at the rate 
of about 600 pounds per minute. The average tests of the 
briquettes of each sample should be taken as the strength, ex- 
cluding any results which are manifestly faulty. 

Constancy 0) Volume. — The object is to develop those quali- 
ties which tend to destroy the strength and durability of a cement. 
As it is highly essential to determine such qualities at once, tests 
of this character are for the most part made in a very short time, 
and are known, therefore, as accelerated tests. Failure is re- 
vealed by cracking, checking, swelling, or disintegration, or all 
of these phenomena. A cement which remains perfectly sound 
is said to be of constant volume. 

Tests for constancy of volume are divided into two classes; 
(1) normal tests, or those made in either air or water main- 
tained at about 21 C. (70 F.), and (2) accelerated tests, or 
those made in air, steam, or water at a temperature of 45 C, 
(11 5 F.) and upward. The test-pieces should be allowed to re- 
main twenty-four hours in moist air before immersion in water 
or steam, or preservation in air. 

For these tests, pats, about 7 J cm. (2.95 inches) in diameter, 
1} cm. (0.49 inch) thick at the centre, and tapering to a thin 
edge, should be made, upon a clean glass plate [about 10 cm. 
(3.94 inches) square], from cement paste of normal consistency. 



190 EXPERIMENTAL ENGINEERING. [§ 120. 

Normal Test. — A pat is immersed in water maintained as 
near 21 C. (70 F.) as possible for 28 days, and observed at 
intervals. A similar pat is maintained in air at ordinary tem- 
perature and observed at intervals. 

Accelerated Test. — A pat is exposed in any convenient way 
in an atmosphere of steam, above boiling water, in a loosely 
closed vessel for three hours. 

To pass these tests satisfactorily, the pats should remain 
firm and hard, and show no signs of cracking, distortion, or 
disintegration. Should the pat leave the plate, distortion may be 
detected best with a straight-edge applied to the surface which 
was in contact with the plate. In the present state of our 
knowledge it cannot be said that cement should necessarily be 
condemned simply for failure to pass the accelerated tests, 
nor can it be considered entirely satisfactory if it has passed 
these tests. 

120. Specifications for Cement. — The following specifica- 
tions were adopted by the committee of the American Society for 
Testing Materials, Nov. 14, 1904: 

General Conditions. — 1. All cement shall be inspected. 

2. Cement may be inspected either at the place of manufacture or on 
the work. 

3. In order to allow ample time for inspecting and testing, the cement 
should be stored in a suitable weather-tight building having the floor properly 
blocked or raised from the ground. 

4. The cement shall be stored in such a manner as to permit easy access 
for proper inspection and identification of each shipment. 

5. Every facility shall be provided by the contractor and a period of at 
least twelve days allowed for the inspection and necessary tests. 

6. Cement shall be delivered in suitable packages with the brand and 
name of manufacturer plainly marked thereon. 

7. A bag of cement shall contain 94 pounds of cement net. Each barrel 
of Portland cement shall contain 4 bags, and each barrel of natural cement 
shall contain 3 bags of the above net weight. 

8. Cement failing to meet the seven-day requirements may be held await- 
ing the results of the twenty-eight-day tests before rejection. 

9. All tests shall be made in accordance with the methods proposed by 
the Committee on Uniform Tests of Cement of the' American Society of 



§ 120.] TESTING MATERIALS OF CONSTRUCTION. 191 

Civil Engineers, presented to the Society January 21, 1903, and amended 
January 20, 1904, with all subsequent amendments thereto. 

10. The acceptance or rejection shall be based on the following require- 
ments: 

11. Natural Cement. — Definition. — This term shall be applied to the 
finely pulverized product resulting from the calcination of an argillaceous 
limestone at a temperature only sufficient to drive off the carbonic acid gas. 

12. Specific Gravity. — The specific gravity of the cement thoroughly 
dried at ioo° C. shall be not less that 2.8. 

13. Fineness.— It shall leave by weight a residue of not more than 10% 
on the No. 100 sieve, and 30% on the No. 200. 

14. Time of Setting. — It shall develop initial set in not less than ten minutes, 
and hard set in not less than thirty minutes nor more than three hours. 

15. Tensile Strength. — The minimum requirements for tensile strength 
for briquettes one inch square in cross-section shall be within the following 
limits, and shall show no retrogression in strength within the periods specified:* 

NEAT CEMENT. 
Age Strength. 

24 hours in moist air 50-100 lbs. 

7 days (1 day in moist air, 6 days in water) 100-200 " 

28 days (1 day in moist air, 27 days in water) 200-300 " 

ONE PART CEMENT, THREE PARTS STANDARD SAND. 

7 days (1 day in moist air, 6 days in water) 25-75 " 

28 days (1 day in moist air, 27 days in water) 75~i5o " 

16. Constancy of Volume. — Pats of neat cement about three inches in 
diameter, one-half inch thick at centre, tapering to a thin edge, shall be kept 
in moist air for a period of twenty-fours hours. 

(a) A pat is then kept in air at normal temperature. 

(b) Another is kept in water maintained as near 70° F. as practicable. 

17. These pats are observed at intervals for at least 28 days, and, to 
satisfactorily pass the tests, should remain firm and hard and show no signs 
of distortion, checking, cracking, or disintegrating. 

18. Portland Cement. — Definition. — This term is applied to the finely 
pulverized product resulting from the calcination to incipient fusion of an 
intimate mixture of properly proportioned argillaceous and calcareous mate- 

* For example, the minimum requirement for the twenty-four-hour neat-cement 
test should be some specified value within the limits of 50 and 100 pounds, and 
so on for each period stated. 



192 EXPERIMENTAL ENGINEERING. [§ 120 

rials, and to which no addition greater than 3% has been made subsequent 
to calcination. 

19. Specific Gravity. — The specific gravity of the cement, thoroughly 
dried at ioo° C, shall be not less than 3.10. 

20. Fineness. — It shall leave by weight a residue of not more than 8% 
on the No. 100 sieve, and not more than 25% on the No. 200. 

21. Time of Setting. — It shall develop initial set in not less than thirty 
minutes, but must develop hard set in not less than one hour nor more than 
ten hours. 

22. Tensile Strength. — The minimum requirements for tensile strength 
for briquettes one inch square in section shall be within the following limits, 
and shall show no retrogression in strength within the periods specified:* 

NEAT CEMENT. 
Age. Strength. 

24 hours in moist air 150-200 lbs. 

7 days (1 day in moist air, 6 days in water) 450-550 " 

28 days (1 day in moist air, 27 days in water) 550-650 " 

ONE PART CEMENT, THREE PARTS SAND. 



7 days (1 day in moist air, 6 days in water) 150-200 

28 days (1 day in moist air, 27 days in water).. ...... 200-300 



a 



23. Constancy of Volume. — Pats of neat cement about three inches in 
diameter, one-half inch thick at the centre, and tapering to a thin edge, shall 
be kept in moist air for a period of twenty-four hours. 

(a) A pat is then kept in air at normal temperature and observed at 
intervals for at least 28 days. 

(b) Another pat is kept in water maintained as near 70 F. as practicable, 
and observed at intervals for at least 28 days. 

(c) A third pat is exposed in any convenient way in an atmosphere of 
steam, above boiling water, in a loosely closed vessel for five hours. 

24. These pats, to satisfactorily pass the requirements, shall remain 
firm and hard and show no signs of distortion, checking, cracking, or dis- 
integrating. 

25. Sulphuric Acid and Magnesia. — The cement shall not contain more 
than 1.75% of anhydrous sulphuric acid (S0 3 ), nor more than 4% of mag- 
nesia (MgO). 

* For example, the minimum requirement for the twenty-four-hour neat-cement 
test should be some specified value within the limits of 150 and 200 pounds, and 
so on for each period stated. 



§ 120.] TESTING MATERIALS OF CONSTRUCTION. I93 

The following observations are taken with respect to each 
briquette : 

Brand of cement 

Temperature of air at mixing* 

Temperature of water at mixing 

Percentage of sand 

" " water 

" " cement.. 

Date of mixing . . 

Time of mixing 

In the log of the tests the following are the headings for 
the columns : No. ; Time of Testing ; Weight of Water ; Ten 
sile Strength ; and Remarks. 

Prof. Lanza of Boston requires a report of the following 
form: 

CEMENT TEST. 



Date of test, 

Date of mixing, 

No. of days set, 

Manner of setting (in air or in water), 

Kind of cement, 

I3rand ...•••■o.. 



Cement. Sand 

Mixture (by wt.), % 

Breaking-strength per sq. in. (tension), . ♦ 
Crushing- load (2-in. cube), ...... 

Signed 



Water, 



............. 



Lime. 
•* % 



The cement-testing laboratory of Berlin, which has perhaps 
the best reputation for this line of work, makes observations as 
shown on the following schedule, which gives the results of 
eleven tests, as given in a paper by P. M. Bruner, before the 
Engineers' Club of St. Louis: 



1 94 



EXPERIMEN TA L ENGINEERING. 



120, 









<u c y 
c5) M 






.So* 
•o a 
£}£ 

(J 75 



091*1 


« 





o 


lO 





O 











o 





ooi'e 


vs. 


CO 


o 




LO 

















m 


o^s'C 


■<§• 


M 




to 


CO 


CI 


o 


o 





o 


* 


oog'S 


T&S. 

•* 


* 


N 


to 


lo 

6\ 


w 


« 











t^ 


oSs'z£ 


^ 
" 


M 


V© 




lo 


VO 


H 


s 


^o 


* 


IN 






a 

S SJ 
£2 



•3|g 



aaniBJadaiax jo asi^ 



•3ui«ds jo 3Tnix 



00 00 ID 

to \o vo m io \o i/> >n 



O N CO vo \o O 

>rtio«MiHHNwcn-4- 












6 be u 
£■§35 £ 
OtsOh 



•axjrj a3d m 3 ! 3 M 



•puBjg 



ro ro ro ro 



*vOM s-t t^co mOOvomnvoOmoo rovo ON O 
CO m « CO LOCO CO OCO O lllNNOflOO mmovS ro io 
CJ\roON Nm o tM\fl o ro o> ro r>. m a r^\© m On ro 



<! <J < ft ft ft ft 



3 Jf 



3 K K 

Oh 



§ 121.] TESTING MA TERIA LS OF CONS TR UCT/ON. I 9 5 

121. Coefficients of Strength. — It is desirable to know in 
advance of the test the probable load the material under in- 
vestigation will safely bear, in order that increments of stress 
may be so proportioned as to make a reasonable number of 
observations. It is also often desirable to know how the 
results obtained compare with the standard values for the 
material under investigation. To provide this information a 
brief statement of the results of various tests are tabulated in 
the Appendix. These results are mainly obtained from " Ma- 
terials of Construction," by R. H. Thurston (3 vols.; N. Y., 
Wiley & Son); and from " Applied Mechanics," by Prof. G. 
Lanza (N. Y., J. Wiley & Son) ; and •' Materials of Engineer 
ing," by Prof. W. H. Burr (N. Y., J. Wiley & Son). These 
books will be found of great value for reference in the testing- 
laboratory. 



CHAPTER VI. 
FRICTION— TESTING OF LUBRICANTS. 

122. Friction. — This subject is of great importance to en- 
gineers, since in some instances it causes loss of useful work, 
and in other instances it is utilized in transmission of power. 
The subject is intimately connected with that of measurement 
of power by dynamometers, treated in Chapter VII. ; in con- 
nection with these two chapters, the student is advised to read 
" Friction and Lost Work in Machinery and Mill-work," by R. 
H. Thurston ; N. Y., J. Wiley & Sons. 

Definitions. — Friction, denoted by F, is the resistance to 
motion offered by the surfaces of bodies in contact in a direc- 
tion parallel to those surfaces. 

The normal force ', denoted by R, is the force acting perpen- 
dicular to the surfaces, tending to press them together. 

The coefficient of friction^ f is the ratio of the friction, F, to 
the normal force, R ; that is, f = F -^ R. 

The total pressure, P, is the resultant of the normal pressure, 
R, and of the friction, F, and its obliquity or inclination to the 
common perpendicular of the surfaces is the angle of repose> 
ox friction, whose tangent is the coefficient of friction. 

The angle of repose ox friction, <p, is the inclination at which 
a body would«start if resting on an inclined plane. It is easy to 
show* that for that condition, if Wis the weight of the body, 

Wqoscj)=-R\ also, W sin <f) = F\ 



* See Mechanics, by I. P. Church; p. 164. 

196 



§ 1 24.] FRICTION— TESTING OF LUBRICANTS. 

and since / = F -r- R, 

W sin (p 



19; 



/=! 



W^COS 



— tan 0. 



It has been shown by experiment that for sliding friction 
(1) the coefficient /is independent of R ; (2) it is greater at the 
instant of starting than after it is in motion ; (3) it is independ- 
ent of the area of rubbing surfaces ; (4) it is diminished by 
lubrication ; (5) it is independent of velocity. 

123. Classification and Notation.— The subject of friction 
is naturally divided into the following sub-heads, all of which 
are intimately connected with methods of lubrication : 

A. Friction of rest, occurring when a body is about to start. 
It is the resistance to change of position. 

B. Friction of motion, occurring during uniform motion, and 
being less than the friction of rest. 

The second kind, or friction of motion, is of principal im- 
portance, and consists of — 

1. Sliding friction. 

a. Bodies sliding on a plane. 

b. Axles or journals rolling in boxes. 

c. Pivots turning on a plane step. 

2. Rolling friction. 

a. One body rolling over a plane. 

b. One body rolling over another. 

124. Formulae and Notation. 



a = angle of inclination of plane; 
<p = angle of friction; 
=. arc of contact on journal; 
/? = inclination of force with plane; 
R = normal force on a plane; 
/= coefficient of friction; 



r = radius of journal; 

/ = length of journal; 

a = space passed through; 

p = intensity of pressure per sq. in,l 
P = total pressure; 
W = weight of the body. 



The most important formulae relating to friction can be 

tabulated as follows : 



198 



EXPERIMENTAL ENGINEERING. 
TABLE OF USEFUL FORMULAE. 



[§ 126. 





Force of friction 


F 

f 
±D 

F 


fW=W tan a=Wtsin <p. 

Tan a = tan <p = \/ W* — R* -5- R. 
W (sin a ± / cos a) -*- (cos /? ± / 
sin £). 


c 


Coefficient of friction 


Cm 


Oblique force 


c 


Force of friction 





fR = W sin <p=/W-i- Vi+/*- 






"c3 

c 

1 v. 

V s 

>,„ 


Square of reaction of bearing. 

Weight on journal (squared) . . 

Moment of friction 

Work of friction per minute. . . 


iV 2 

vm 

M 
U 


W* - F* = W\\ - sin 2 0) = W* 

cos 2 (p. 
N* + F* = N\i +/ 2 ) = F\i +/*) 


_3 bfl 

.5 


Fr = Wr sin <f> =/Wr -4- |/i +/». 
War sin <p = 2%nrW sin <f> = 
27tnr/IV-r- |/i-r-/ 2 . 


"c3 

c 
1- 
3 


>> 

t> 
u 

Cm 


Weight on journal (general). . . 

Intensity of pressure at 6=90° 

Weight, perfect fit of journal. . 

Pressure per square inch 

Maximum pressure per sq. inch 

Total pressure on bearing .... 

Total force of friction 

Work of friction 


w 

p' 

w 
p 

pnt 
P 

F 

ip 

M 
U 


/» + « 
/ plr cos QdQ. 

p -T- cos 0. 

p'lr / cos 2 BdQ = 1.57/^. 

•J-y#r 
0.64 IV cos 6 -T- Ir. 
0.64 W -f- /y. 

0.64 w/ cosQdQ = i.2TlV. 

fP'W= 1.27/W. 

I.2J/W (space). 

P'/r = i.vjfWr. 

Ma = 1.27/ Wr = 2.^71 fnrW. 




Moment of friction 




Work of friction per minute . . 




Maximum pressure per sq. inch 
Total pressure 


P' 

P' 

F 

M 

U 


W-t-2/r. 
p'litr -\itW ' = 1.57 JF. 
P'f =t.StfW. 

P'fr= i.si/Wr. 

Ma = \.e>7afWr— 2it/Wrn. 


^0 


Total force of friction 

Moment of friction 


3 2 


Work of friction per minute. . . 



125. Friction of Journals in V or Triangular Bearings. 
— Force of friction F= P cos sin -f- cos <*, in which /> 
equals the force transmitted through the shaft. When cos 
= 1, F — P sin -f- cos a, 

126. Friction of Pivots on Flat Rotating Surfaces.— 
Intensity of pressure = / ; total pressure = P. Moment of 



§ 128.] FRICTION— TESTING OF LUBRICANTS. 1 99 

friction, M — \fPr. Work of friction, U = ^nnfPr. For a 
conical pivot, M = ^fPr -r- sin a. a = \ angle of cone. 

For Friction on a Flat Collar. — Moment of friction, M = 
IfP^-r'^ir'-r"); r= radius of collar ; r'= radius of shaft 
on which it is fitted. 

127. Friction of Teeth— Rolling Friction. — Work lost in 
a unit of time, U=nFPs, in which s equals the sliding or slip- 
ping ; n, number of teeth ; other terms as before. For in 
volute teeth, in which C 1 = length of arc of approach, C % that 
of arc of recess, the obliquity of action, r, and r 3 respective 
pitch-radii, we have for involute teeth 

U = nfPs 6= nfP(C? + C*)(^ + l ~) + 2 cos ft 



1 ' a' 



This is nearly accurate for any teeth. (-See article " Me- 
chanics," Encyc. Britannica.) 

128. Friction of Cords and Belts— Sliding Friction.— 
Let T x be the tension on driving side of belt, T 2 on the loose 
side, Tthe tension at any part of the arc of contact; let 6 be 
the length of the arc of contact divided by the radius, i.e., ex- 
pressed in circular measure ; let c equal the ratio of the arc of 
contact to the entire circumference; let d equal the number of 
degrees in the arc of contact, e the base of the Napierian 
logarithms = 2.71828, m the modulus of the common loga- 
rithms = 0.434295 ; let F equal the force of friction. 

_ nr d nd 

e '-78~o7 = T8o' -W 

_ d 
'-3S-2? W 

a = = 360& (c) 

it 

The tension at any point, dT, is equal to the resistance TfdO. 

Hence 

dT = Tfdd, ....... (d) 

or 



200 EXPERIMENTAL ENGINEERING. [§ 1 29. 

This integrated between limits T 1 and 7!, gives 

T 1 T 

fd = log e -^ = — (common) log ^ ; . • . ■ . (*) 

hence 

rp fndm 

■* 2 

From the nature of the stress, 

F=T t -.T. fe) 

-~? = the number corresponding to the logarithm, which is 

■* 2 

1 /•/, fndm 

equal fdm y or — — , or 2itfcm. 

Substituting numerical values, 

fdm = 0.434/0, ^-^ == 0.00758/5/, and 27r/cm = 2^2SS/c. 
From equations (/), 

common log f ~J = 0434/9 = 2.7288/fc. 

By solving equations (/) and (g), 

T > = F B=i W 

T .= F TT=? « 

129. Friction of Fluids (1) is independent of pressure ; 
(2) proportional to area of surface ; (3) proportional to square 
of velocity for moderate and high speeds and to velocity for 
low speeds ; (4) is independent of the nature of the surfaces ; 
(5) is proportional to the density of the fluid, and is related to 
viscosity. 

The resistance to relative motion in case of fluid friction. 

R=/AV 2 = zghfA =fkwA ; 



§ 131.] FRICTION— TESTING OF LUBRICANTS, 201 

the work of friction, 

17= Rs = RVt =/A VH = fAhwVt. 

In the above formulae R = resistance of friction, A = area 
of surface, F= velocity of slipping, h = head corresponding 
to velocity, w = weight, f t«he resistance per unit of area of 

surface,/ 7 = coefficient of liquid friction, f = -^— . 

Viscosity and density of fluids do not affect to any appreci- 
able extent the retardation by friction in the rate of flow, but 
have some influence upon the total expenditures of energy. 
Molecular or internal friction also exists. 

130. Lubricated Surfaces. — Lubricated surfaces are no 
doubt to be considered as solid surfaces, wholly or partially 
separated by a fluid, and the friction will vary, with different 
conditions, from that of liquid friction to that of sliding fric- 
tion between solids. Dr. Thurston * gives the following laws, 
applicable to perfect lubrication only: 

1. The coefficient of friction is inversely as the intensity of 
the pressure, and the resistance is independent of the pressure. 

2. The coefficient varies with the square of the speed. 

3. The resistance varies directly as the area of journal and 
bearing. 

4. The friction is reduced as temperature rises, and as the 
viscosity of the lubricant is thus decreased. 

Perfect lubrication is not possible, and consequently the 
laws governing the actual cases are likely to be very different 
from the above. The coefficient of friction in any practical 
case is likely to be made up of the sum of two components, 
solid and fluid friction. 

TESTING OF LUBRICANTS. 

131. Determinations required. — The following determina- 
tions are required in a complete test of lubricants : 

1. The composition, and detection of adulteration. 

2. The measurement of density. 

* See Friction and Lost Work, by Thurston. 



202 EXPERIMENTAL ENGINEERING. £§ 133, 

3. The determination of viscosity. 

4. The detection of tendency to gum. 

5. The determination of temperatures of decomposition, 
vaporization, ignition, and solidification. 

6. The detection of acids. 

7. The measure of the coefficient of friction. 

8. The determination of durability and heat-removing 
power. 

9. The determination of its condition as to grit and foreign 
matter. 

132. Adulteration of Oils. — Adulteration can be detected 
only by a chemical analysis.* 

Animal oils may be distinguished from vegetable oils by 
the fact that chlorine turns animal oil brown and vegetable oil 
white. 

133. Density of Oils. — The density or specific gravity is 
usually obtained with a hydrometer (see Fig. 10 1) adapted for 
this special purpose, and termed an oleometer. The distance 

that it sinks in a vessel of oil of known temperature 
is measured by the graduation on the stem ; from 
this the specific gravity of the oil may be found. 

The density is usually expressed in Beaume's hy- 
drometer-scale, which can be reduced to correspond- 
ing specific gravities as compared with water by a 
table given in the Appendix. 

Beaume's hydrometer is graduated in degrees to 
accord with the density of a solution of common 
salt in water ; thus, for liquids heavier than water 
the zero of the scale is obtained by immersing in 
pure water; the five-degree mark by immersing in a 
five-per-cent solution ; the ten-degree mark in a ten- 
Fig. 101. p er _ cen t solution ; etc. For liquids lighter than 

Hydrombter. r ......... 

water the zero-mark is obtained by immersing in a 
ten-per-cent solution of brine ; the ten-degree mark by im- 
mersing in pure water. After obtaining the length of a 

degree the stem is graduated by measurement. 

— - 

* See Friction and Lost Work, by R. H. Thurston. 



§ J 35-] FRICTION— TESTING OF LUBRICANTS. 203 

The density may be found by obtaining the loss of 
weight of the same body in oil and in distilled water. The 
ratio of loss of weights will be the density compared with 
water. 

It may also be obtained by weighing a given volume on a 
pair of chemical scales. The density of animal oils varies from 
.62 to .89; sperm-oil at 39 F. has a density of .8813 to .8815 ; 
rape-seed oil has a density of .9168; lard-oil (winter) has a 
density of .9175 ; cotton-seed oil a density of .9224 to .9231 for 
ordinary, and of .9128 for white winter; linseed-oil, raw, has a 
density of .9299; castor-oil, pure cold-pressed, a density of 
.9667. 

134. Method of finding Density. — A. With Hydrometer 
Thermometer, and Hydrometer Cylinder. 

Method. — 1. Clean the cylinder thoroughly, using benzine 
fill first with distilled water. Set the whole in a water-jacket, 
and bring the temperature to 6o° F. Obtain the reading of the 
hydrometer in the distilled water and determine its error. 

2. Clean out the cylinder, dry it thoroughly, and fill with 
the oil to be tested ; heat in a water-jacket to a temperature of 
60 ° F., and obtain reading of hydrometer ; also obtain reading, 
at temperatures of 40 , 8o°, ioo°, 125 , and 150 , and plot a 
curve showing relation of temperature and corrected hydrome- 
ter-reading. 

Reduce hydrometer-readings to corresponding specific 
gravities, by table given in Appendix. 

B. Weigh on a chemical balance the same volume of dis- 
tilled water at 6o° F., and of the oil at the same temperature; 
and compute the specific gravity. 

C. Weigh the same metallic body by suspending from the 
bottom of a scale-pan of a balance : 1. In air; 2. In water ; 3. 
In the oil at the required temperature. Carefully clean the 
body with benzine after immersing in the oil. The ratio of the 
loss of weight in oil to that in water will be the density. 

*35- Viscosity. — Viscosity of oil is closely related but not 
proportional to its density. It is also closely related, and in 
many cases it is inversely proportional, to its lubricating prop- 



204 



EXPERIMENTAL ENGINEERING. 



[§ 136. 



erties. The relation of the viscosities at ordinary temperatures 
is not the same as for higher temperatures, and tests for vis- 
cosity should be made with the temperatures the same as those 
in use. The less the viscosity, consistent with the pressure to 
be used, the less the friction. 

The viscosity test is considered of great value in determin- 
ing the lubricating qualities of oils, and it is quite probable 
that by means of it alone we could determine the lubricating 
qualities to such an extent that a poor oil would not be accepted 
nor a good oil rejected. It is, however, in the present method 
of performing it, to be considered rather as giving comparative 
than absolute results. 

There are several methods of determining the viscosity 
It is usual to take the viscosity as inversely proportional to its 

,. flow through a standard nozzle 
while maintained at a constant 
or constantly diminishing head 
and constant temperature, a 
comparison to be made with 
water or with some well-known 
oil, as sperm, lard, or rape-seed, 
under the same conditions of 
pressure and temperature. 

136. Viscosimeter. — A pi- 
pette surrounded by a water- 
jacket, in which the water can 
be heated by an auxiliary lamp 
and maintained at any desired 
temperature, is generally used 
as a viscosimeter. Fig. 72 
shows the usual arrangement 
for this test. E is the heater 
fig. io a .-ViscosiTY of Oils. for the jacket-water, BB the 

jacket, A the pipette, C a thermometer for determining the 
temperature of the jacket-water. The oil is usually allowed to 
run partially out from the pipette, in which case the head 
diminishes. Time for the whole run is noted with a stop-watch. 




§ 1 390 



FRICTION— TESTING OF LUBRICANTS. 



205 



In the oil-tests made by the Pennsylvania R. R. Co. the 
pipette is of special form, holding 100 c.c. between two marks, 
— one drawn on the stem, the other some distance from the end 
of the discharge-nozzle. 

137. Tagliabue's Viscosimeter. — In Tagliabue's viscosim- 
eter, shown in Figs. 103 and 104, the oil is 
supplied in a basin C, and trickles down- 
ward through a metal coil, being dis- 
charged at the faucet on the side into a 
vessel holding 50 c.c. The oil is main- 
tained at any desired temperature by 
heating the water in the vessel B sur- 
rounding the coil ; cold water is supplied 
from the vessel A, as required to main- 
tain a uniform temperature. The tem- 
perature of the oil is taken by the ther- 
mometer D. 

138. Gibbs' Viscosimeter. — In the 
practical use of viscosimeters it is found 
that the time of flow of 100 c.c. of the 
same oil, even at the same temperature, ,. 

1 Fig. 103.— Tagliabue's Visco- 

is not always the same, — which is probably simeter. 

due to the change in friction of the oil adhering to the sides of 

the pipette. 

To render the conditions which produce flow more constant, 
Mr. George Gibbs of Chicago surrounds the viscosimeter, which 
is of the pipette form, with a jacket of hot oil. A circulation 
of the jacket-oil is maintained by a force-pump. The oil to 
be tested is discharged under a constant head, which is insured 
by air-pressure applied by a pneumatic trough. The tempera- 
ture of the discharged oil is measured near the point of dis- 
charge. 

139. Perkins' Viscosimeter. — The Perkins Viscosimeter 
consists of a cylindrical vessel of glass, surrounded by a water or 
oil bath, and fitted with a piston and rod of glass. The edges 
of this piston are rounded, so as not to be caught by a slight 
angularity of motion. The diameter is one-thousandth of an 




206 



EXPERIMENTAL ENGINEERING. 



L§ ML 



inch less than that of the cylinder. In practice the cylinder is 
filled nearly full of the oil to be tested, and the piston inserted. 




Fig. 104. — Tagliabue's Viscosimeter. 

The time required for the piston to sink a certain distance into 
the oil is taken as the measure of the viscosity.* 

140. Stillman's Viscosimeter. — Prof. Thomas B. Stillman 
of Stevens Institute uses a conical vessel of copper, 6f inches 
in length and if inches greatest diameter, surrounded by a 
water-bath, and connected to a small branch tube of glass, 
#hich is graduated in cubic centimeters ; the time taken for 
25 c.c. to flow through a bottom orifice -f x of an inch in diam- 
eter is taken as the measure of the viscosity, during which time 
the head changes from 6 to 5 inches. Prof. Stillman makes all 
comparisons with water, which is the most convenient and 
uniform standard. The temperature of the oil is taken at 
about the centre of the viscosimeter. 

141. Viscosimeter with Constant Head A form of 

viscosimeter which possesses the advantage of having a con- 
stant head for flow of oil regardless of the quantity in the 
instrument, as made by Tinius Olsen & Co. of Philadelphia, 

* See paper by Prof. Denton, Vol. IX., Transactions of Am. Society of 
Mechanical Engineers. 



I4i.] 



FRICTION— TESTING OF LUBRICANTS. 



207 



is shown in the next figure. It is simple in form and can be 
very readily cleaned. It is provided with a jacket, and oils 
may be tested at any temperature. This instrument is now 
the principal standard used in the 
Sibley College Laboratories. 

Description. — A is a cup similar in 
construction to that of the kerosene 
reservoir of a* students' lamp, with a 
capacity of about 125 c.c, and is sur- 
rounded with a jacket D, in which may 
be placed insulating materials to main- 
tain a constant temperature while the 
oil is flowing; C is a thermometer-cup, 
to the bottom of which is secured a 
small cap containing the orifice F ; N 
is a channel connecting chamber con- 
taining A with C; B is one of four 
small tubes which admit air to the in- 
terior of the cup A and thus maintain 
atmospheric pressure on oil in it; this 
action secures a constant level of the 
surface of the oil in the cup C and 
the surrounding space, at the height of the lower opening 
in the tube B. H is a valve to retain oil in A while placing 
it into D. M and N are brackets serving as guides for valve- 
stem K. 

The mechanism L, G, G is a device for opening and 
closing the orifice F readily, and is held in a closed position 
by spring catch L. 

The instrument is supported by three legs about eight 
inches in length. 

Operation.— Withdraw cup A, fill it in an inverted posi- 
tion with the oil, hold valve H on its seat while reinserting 
the cup into its former place as seen in figure, in which latter 
operation the valve H is raised and the oil allowed to flow 
out of A until chambers N and C are filled a little above 




Fig. 105. — Viscosimeter 



208 EXPERIMENTAL ENGINEERING. [§ 1 4 1. 

lower opening of tube B. A beaker graduated in c.c.'s, of 
capacity of about no c.c, is placed under F; L is released 
and G allowed to drop, permitting oil to flow through F freely 
into the beaker. When oil in C falls below the bottom of 
tube B, air is admitted to the top of the oil in A and oil flows 
out until it rises a little above tube B again, when flow out 
of A is stopped until the level falls below B again. This 
action continues throughout entire run, intermittently but so 
rapidly that a constant head is maintained at F. 

In C a thermometer is suspended so that its bulb is 
immersed in the oil, by which means the temperature of oil 
can be observed immediately before flowing out of orifice F y 
which is essential in ascertaining the viscosity of the oil. 
The oil may be heated in the viscosimeter by applying a 
Bunsen burner, but it is usually more conveniently heated in 
a separate vessel until it has attained the proper temperature. 

Method of Conducting a Test. — Since water is taken as the 
standard of comparison, the amount of flow for 100 c.c. is 
first determined. Clean apparatus thoroughly, then fill A 
with water, allow 100 c.c. to flow and note time; similarly 
make four or five runs so as to get a fair average. 

Wipe apparatus again thoroughly dry and proceed in a 
similar manner, using oil at different temperatures. The 
jacket should be heated a little with every movement of tem- 
peratures. The oil should be heated in a separate vessel and 
then poured into A. 

The ratio of time of flow of a quantity of oil to time of 
flow of an equal quantity of water measures the relative 
viscosity of the given sample of oil to that of water at the 
given temperature. For comparing the results obtained with 
this instrument, the time of flow of 100 c.c. only need be 
known, since all the instruments are standardized. 

A simple form of viscosimeter has been used with success 
by the author, consisting of a copper cup in form of a frustum 
of a cone, having dimensions as follows: bottom diameter 
I.25 inches, top diameter 1.95 inches, depth 6 inches. The 



§ I43-] 



FRICTION— TESTING OF LUBRICANTS. 



209 



flow takes place through a sharp-edged orifice in the centre 
of the bottom ^ inch in diameter. The whole height is 6£ 
inches. The instrument when made of copper requires a 
glass oil-gauge, showing the height of the oil in the viscosi- 
meter. This should be connected to the viscosimeter 3 
inches from the bottom. The time for the flow of 100 c.c. 
is taken as the measure of the viscosity, during which time 
the head changes from 6 to about 3.5 inches, the area of 
exposed surface diminishes at almost exactly the rate of 
decrease of velocity of flow, so that the fall of level is very 
nearly constant. 

The comparative number of vibrations of a pendulum 
swinging freely in the air, and when immersed in an oil dur- 
ing a given time, is also said to afford a valuable means of 
determining the viscosity. 

142. Viscosity Determinations of Oil, by Prof. Thomas 
B. Stillman. 



Fluid. 



Water 

Prime lard-oil 

No. 1 '* " 

Gelatine-oil 

Rosin-oil, ist run 

" " 2d run 

Sperm-oil 

Castor-oil 

Cotton-seed oil — winter... 
" " " summer. 

Rape-seed oil 

Olive-oil 



Time of Flow in Seconds of 25 
c.c. through Orifice as explained. 



20 C. 
68° F. 

15 

55 

70 



240 
70 

33 
39 
5i 
57 
7i 
63 



so°c. 


IOO° C. 


122° F. 


212° F. 


29 


19 


30 


18 


8O 


19 


23 


15 


22 


16 


24 


17 


26 


27 


27 


18 


26 


20 


24 


18 



16 

16 
360 

15 

14 

15 
16 

15 
15 
16 
16 



Viscosity 
compared 
with water 
at 20° C 
(68° F.). 



I.O 
3-6 
4.6 

16.O 
4.6 
2.2 
2.6 

3-4 
3.8 
4.2 
4-7 



143. Method of measuring Viscosity. — Apparatus. Stop- 
watch and viscosimeter. Fill the jacket of the viscosimeter 
with water and arrange for the maintenance of the same at any 
desired temperature. This is most conveniently done by cir« 
culation from a water-bath. Fill the viscosimeter with the oil 



210 EXPERIMENTAL ENGINEERING. [§ 144- 

to a point above the upper or initial mark. Allow the oil to 
run out, noting accurately with the stop-watch the exact time 
required to discharge a given amount. Make determinations 
at 6o°, ioo°, and 150 F., two for each temperature. Clean 
the apparatus thoroughly at the beginning and end of the test, 
using benzine or alkali to remove any traces of oil. 

143. Gumming or Drying. — Gumming or drying is a con- 
version of the oil into a resin by a process of oxidation, and 
occurs after exposure of the oils to the air. In linseed and the 
drying oils it occurs very rapidly, and in the mineral oils very 
slowly. 

Methods of Testing. — Nasmyttis Apparatus. — An iron plate 
six feet long, four inches wide, one end elevated one inch. 
Six or less different oils are started by means of brass tubes at 
the same instant from the upper end : the time taken until the 
oil reaches the bottom of the plane is a measure of its gum- 
ming property. 

Bailey s Apparatus consists of an inclined plane, made of a 
glass plate, arranged so that it may be heated by boiling water. 
A scale and thermometer is attached to the plane. Its use is 
the same as the Nasmyth apparatus. 

This effect may also be tested in the Standard Oil-testing 
Machine by applying fresh oil, making a run, and noting the 
friction ; then exposing the axis to the effect of the air for a 
time, and noting the increase of friction. In all cases a com- 
parison must be made with some standard oil. 

144. The Flash-test. — The effect of heat is in nearly 
every case to increase the fluidity of oils and to lessen the vis- 
cosity ; the temperature at which oils ignite, flash, boil, or 
congeal is often of importance. 

The Flash-test determines the temperature at which oils 
discharge by distillation vapors which may be ignited. The 
test is made in two ways. 

Firstly. With the open cup. — In this case the oil to be tested 
k placed in an open cup of watch-glass form, which rests on a 
sand-bath. The cup is so arranged that a thermometer can 
be kept in it. Heat is applied to the sand-bath, and as the oil 



§144-] 



FRICTION— TESTING OF LUBRICANTS. 



211 



becomes heated a lighted taper or match is passed at intervals 
of a few seconds over the surface of the oil, and at a distance 
of about one half-inch from it. At the instant of flashing the 
temperature of the water-bath is noted, which is the tempera- 
ture of the " flash-point." 

Fig. 1 06 shows Tagliabue's form of the open cup, in which 
heat is applied by a spirit-lamp to a water or sand bath sur- 
rounding the cup containing the oil. 

The method of applying the match is found to a have great 
influence on the temperature of the flash-point, and should be 
distinctly stated in each case. When the vapor is heavier than 




CtNlRAL BUREAU OF ENO' 

Fig. 106.— Open Cup. 




Fig. 107.— Closed Cup for Flashing-point. 



air, a lower flash-point will be shown by holding n?,ar one edge 
of the cup. 

Secondly. With the closed oil-cup. — Fig. 107 is a view of Tag- 
liabue's closed cup for obtaining the flash-point ; in this instru- 
ment the oil is heated by a sand-bath above a lamp. The 
thermometer gives the temperature of the oil, and the match 



212 EXPERIMENTAL ENGINEERING. [§ 1 46. 

applied from time to time at the orifice d, which in the inter- 
vals can be covered with a valve, determines the flash-point. 

The open cup is generally preferred to the closed one as 
giving more uniform determinations, and it is also more con- 
venient and less likely to explode than the closed one. 

Method of Testing. — Put some dry sand or water in the outer 
cup and some of the oil to be tested in the small cup. Light 
the lamp and heat the oil gently — at the rate of about 50 F. in 
a quarter of an hour. At intervals of half a minute after a 
temperature of ioo° F. is. attained, pass a lighted match or 
taper slowly over the oil at a distance of one half inch at the 
surface. The reading of the thermometer taken immediately 
before the vapor ignites is the temperature of the flash-point. 

With the closed cup the method is essentially the same. 
The lighted taper is applied to the tube leading from the oil 
vessel, the valve being opened only long enough for this pur- 
pose. 

145. Method of Determining the Burning-point. — The 
burning-point is determined by heating the oil to such a tem- 
perature, that when the match is applied as for the flash-test 
the whole of the oil will take fire. The reading of the ther- 
mometer just before the match is applied is the burning-point. 

With Open Cup. — Apparatus: Open cup of watch-glass 
form ; thermometer suspended so that bulb is immersed in 
cup ; outer vessel filled with sand or water, on which the open 
vessel rests; lamp to heat the outer vessel. 

Method. — The burning-point is found in the same manner 
as the flash-point, with the open cup, the test being continued 
until the oil takes fire when the match is applied. The last 
reading of the thermometer before combustion commences is 
the burning-point. 

146. Evaporation. — Mineral oil will lose weight by evapo- 
ration, which may be ascertained by placing a given weight in 
a watch-glass and exposing to the heat of a water-bath for a 
given time, as twelve hours. The loss denotes the existence 
of volatile vapors, and should not exceed 5 per cent in good 
oil. Other oils often gain weight by absorption of oxygen. 



§ I47-] FRICTION— TESTING OF LUBRICANTS. 



213 



147. Cold Tests. — Cold tests are made to determine the 
behavior of oils and greases at low temperatures. The method 
of test is to expose the sample while in a wide-mouthed 
bottle or test-tube to the action of a freezing mixture, which 
surrounds the oil to be tested. Freezing mixtures may be 
made with ice and common salt, with ice alone, or with 15 
parts of Glauber's salts, above which is a mixture of 5 parts 
muriatic acid and 5 parts of cold water. The temperature is 
read from a thermometer immersed in the oil. The melting- 
point is to be found by first freezing, then melting. 

Tagliabue has a special apparatus for the cold test of oils 
shown in section in Fig. 108. The oil is placed in the glass 




y^?y 




Fig. 108.— Tagliabue's Cold-test Apparatus. 

vessel, which is surrounded with a freezing mixture. The 
glass containing the oil can be rocked backward and forward, 
to insure more thorough freezing. A thermometer is inserted 
into the oil and another in the surrounding air-chamber ; the 
oil is frozen, then permitted to melt, and the temperature 
taken. 



214 EXPERIMENTAL ENGINEERING. [§ 1 50. 

In making this test considerable difficulty may be experi- 
enced in determining the melting-point, since many of the oils 
do not suddenly freeze and thaw like water, but gradually 
soften, until they will finally run, and during this whole change 
the temperature will continue to rise. This is no doubt due 
to a mixture of various constituents, with different melting- 
points. In such a case it is recommended that an arbitrary 
chill-point be assumed at the temperature that is indicated by 
a thermometer inserted in the oil, when it has attained suffi* 
cient fluidity to run slowly from an inverted test-tube. The 
temperature at the beginning and end of the process of melting 
is to be observed. 

148. Method of Finding the Chill-point. — Apparatus. — 
Test-tube thermometer, and dish containing freezing mixture. 

Method. — Pour the sample to be tested in the test-tube, in 
which insert the thermometer ; surround this with the freezing 
mixture, which may be composed of small particles of ice 
mixed with salt, with provision for draining off the water. 
Allow the sample to congeal, remove the test-tube from the 
freezing mixture, and while holding it in the hand stir it gently 
with the thermometer. The temperature indicated when the 
oil is melted is the chill-point. 

In case the operation of melting is accompanied with a dis, 
tinct rise of temperature, note the temperature at the begin- 
ning and also at the end of the process of melting. 

In report describe apparatus used and the methods of test- 
ing. 

149. Oleography. — An attempt has been made to deter- 
mine the properties of oil by cohesion-figures, by allowing 
drops of oil to fall on the surface of water, noting the time re- 
quired to produce certain characteristic figures, also by noting 
the peculiar form of these figures. 

Electrical Conductivity is different for the different oils, and 
this has been proposed as a test for adulteration. 

150. Acid Tests. — Tests for acidity may be made by ob- 
serving the effects on blue litmus-paper ; or better by the fol- 
lowing method described by Dr. C. B. Dudley : Have ready (1) 



§ 151.] FRICTION— TESTING OF L UBRICANTS. 2 I 5 

a quantity of 95 per cent alcohol, to which a few grains of car- 
bonate of soda have been added, thoroughly shaken and al- 
lowed to settle ; (2) a small amount of turmeric solution ; (3) 
caustic-potash solution of such strength that 31 \ cubic centi- 
meters exactly neutralize 5 c.C. of a solution of sulphuric acid 
and water, containing 40 milligrams H 2 S0 4 per c.c. Now 
weigh or measure into any suitable closed vessel — a four-ounce 
sample bottle, for example — 8.9 grams of the oil to be tested. 
To this add about two ounces No. 1, then add a few drops 
No. 2, and shake thoroughly. The color becomes yellow. 
Then add from a burette graduated to c.c, solution No. 3 un- 
til the color changes to red, and remains so after shaking. 
The acid is in proportion to the amount of solution (3) re- 
quired. The best oils will require only from 4 to 30 c.c. to be 
neutralized and become red. 



COEFFICIENT OF FRICTION OF LUBRICANTS. 

151. Oil-testing Machines. — Measurements of the coefficients 
of friction are made on oil-testing machines, of which various 
forms have been built. These machines are all species o. 
dynamometers, which provide (1) means of measuring the total 
work received and that delivered, the difference being the work 
of friction ; or (2) means of measuring the work of friction 
directly. Machines of the latter class are the ones commonly 
employed for this especial purpose. 

Rankine's Oil-testing Machine. — Rankine describes two 
forms of apparatus for testing the lubricating properties of oil 
and grease. 

I. Statical Apparatus. — This consists of a short cylindrical 
axle, supported on two bearings and driven by pulleys at 
each end. In the middle of the axle a plumber-block was 
rigidly connected to a mass of heavy material, forming a 
pendulum. The lubricant to be tested was inserted in the 
plumber-block attached to the pendulum, and the coefficient 
of friction determined by its deviation from a vertical. In this 
machine the axle was provided with reversing-gears, so that it 



2l6 . EXPERIMENTAL ENGINEERING. [§ 1 5 1. 

could be driven first in one direction and then in the opposite. 
With this class of machine, if r equal the radius of the journal, 
R the effective arm of the pendulum, P the total force acting 
on the journal, the angle with the vertical, we shall have 
the product of the force W into the arm R sin equal to the 
moment of resistance Fr. That is, 

Fr = WR sin 0, 

from which 

/ - p - p r ~ • 

II. Dynamic or Kinetic Apparatus. — In this case a loose 
fly-wheel of the required weight is used instead of the pendu- 
lum. The bearings of journals and of fly-wheel are lubricated; 
then the machine is set in motion at a speed greater than the 
normal. The driving-power is then disengaged, and the fly- 
disk rotates on the stationary axis until it comes to rest. The 
coefficient of friction is obtained by measuring the retardation 
in a given time. Thus, let W equal the weight of the fly- 
wheel, k its radius of gyration, so that Wk? ~ g equals its 
moment of inertia. Let n equal number of revolutions at 
beginning, and n' at end of period /. Then the retardation in 
angular velocity per second is 

2n(n — n') -s- t ; 

the moment producing retardation, 

If we neglect the resistance of the air, this must equal the 

moment of friction fWr. 
Equating these values, 

J gfr 



§ 152.] 



FRICTION— TESTING OF LUBRICANTS. 



217 



In case the moment of inertia and radius of gyration are un- 
known, they may be found as in Article 53, page 80. 

152. Thurston's Standard Oil-testing Machine. — This 
machine permits variation in speed and in pressure on the 
journal ; it also affords means of supplying oil at any time, of 
reading the pressure on the journal, and the friction on grad- 
uated scales attached to the instrument. 





^W*^.NC*».W>t 



Fig. 109 —Section of Thurston's 
Oil-testing Machine. 



Fig. iio. — Perspective View of Thurston's 
Oil-testing Machine. 



This machine, as shown in the above cuts, Figs. 109 and 1 10, 
consists of a cone of pulleys, C, for various speeds carried be- 
tween two bearings, B, B' , and connected to an overhanging 
axis, F\ on this overhanging part is a pendulum, H> with 
plumber-block in which the axis is free to turn ; the pendulum 
is supported by brasses which are adjustable and which may 
be set to exert any given pressure by means of an adjusting 
screw, !£', acting on a coiled spring within the pendulum. 
The pressure so exerted can be read directly by the scale M y 
attached to the pendulum ; a thermometer, Q, in the upper 
brass gives the temperature of the bearings. The deviation 



21 8 EXPERIMENTAL ENGINEERING. ]% I 53. 

of the pendulum is measured by a graduated arc, PP\ fastened 
to the frame of the machine. The graduations of the pendu- 
lum scale M show on one side the total pressure on the jour- 
nal P, and on the other the pressure per square inch, p ; those 
on the fixed scale, PP', show the total friction, F; this divided 
by the total pressure, P, gives/, the coefficient of friction. 

From the construction of the machine, it is at once per- 
ceived that the pressure on the journal is made up of equal 
pressures due to action of the spring on upper and lower 
brasses, and of the pressure due to the weight of the pendu- 
lum, which acts only on the upper brass. This latter weight 
is often very small, in which case it can be neglected without 
sensible error. 

153. Thurston's Railroad Lubricant-tester. — The 
Thurston machine is made in two sizes ; the larger one, having 
axles and bearings of the same dimensions as those used in 
standard-car construction, is termed the " Railroad Lubricant 
Testing-machine." A form of this machine is shown in the 
following cut, arranged for testing with a limited supply of 
lubricant. (See Fig. ill.) 
Explanation of symbols : 

T, thermometer, giving temperature of bearings. 

R, S, rubber tubes for circulation of water through the 
bearings. 

N, burette, furnishing supply of oil. 

M, siphon, controlling supply of oil. 

P, candle-wicking, for feeding the oil. 

H, copper rod, for receiving oil from G. 
The Railroad Testing-machine, which is shown in section in 
Fig. 1 1 2, differs from the Standard Oil-testing Machine princi- 
pally in the construction of the pendulum. This is made by 
screwing a wrought-iron pipe,/, which is shown by solid black 
shading in Fig. 1 12, into the head K, which embraces the jour- 
nal and holds the bearings a a in their place. In this pipe a 
loose piece, b, is fitted, which bears against the under journal- 
bearing, a'. Into the lower end of the pipe /a piece, cc, is 
screwed, which has a hole drilled in the centre, through which 



§ I 53-] FRICTION— TESTING OF LUBRICANTS. 



2 19 



a rod, f, passes, the upper end of which is screwed into a cap, 
d\ between this cap and the piece cc a spiral spring is placed. 
The upper end of the rod bears against the piece b } which in 
turn bears against the bearing a' . The piece b has a key, /, 
arhich passes through it and the pipe /. This key bears 




Fig. hi.— Thurston's Railroad-Lubricant Testing-machine. 



against a nut, 0, screwed on the pipe. By turning the nut 
the stress on the journal produced by screwing the rod /"can 
be thrown on the key /, and the bearing relieved of pressure, 
without changing the tension on the spring. A counterbalance 
above the pendulum is used when accurate readings are de- 



220 



EXPEKIMEN TA L ENGINEERING. 



[§154. 



sired. The " brasses " are cast hollow, and when necessary a 
stream of water can be passed through to take up the heat, 
and maintain them at an even temperature. 

The graduations on the machine show on the fixed scale. 




Fig. 112.— Section of Railroad Lubricant Testing-machine. 



as in the standard machine, the total friction ; and on the 
pendulum, the total pressures (1) on the upper brasses, (2) on 
the lower brasses, and (3) the sum of these pressures. 

154. Theory of the Thurston Oil-testing Machines. — 
The mathematical formulae applying to these machines are as 
I follows : Let P equal the total pressure on the journal ; / the 
pressure per square inch on projected area of journal ; T the 
tension of the spring; W the weight of the pendulum; r the 
radius of the journal ; R the effective arm of the pendulum ; 



§154-] FRICTION— TESTING OF LUBRICANTS. 22 1 

6 the angle of deviation of the pendulum from a vertical line ; 
F the total force of friction ; / the coefficient of friction ; / 
the length of bearing-surface of each brass. 

Since in this machine both brasses are loaded, the pro- 
jected area of the journal bearing-surface is 2(2r)/ == 4/?*. We 
shall evidently have 



P=2T+ W, (1) 

P 2T+ W 
*=? &=-&—' < 2 > 

By definition /= F + P. 

Since the moment of friction is equal to the external mo- 
ment of forces acting, 

Fr = Pfr=f(2T+W)r= WR sin 6. . . . (3) 
From which 

1 F WR sin 

f=~P = — yp — • (4) 

In the machines WR sin h- r is shown on the fixed scale^ 
and the graduations will evidently vary with sin 0, since 
WR -s- r is constant. 

P, the total pressure, is shown on the scale attached to the 
pendulum. 

In the standard machine the weight of the pendulum is 
neglected, and P = 2 T; but in the Railroad Oil-testing Machine 
the weight must be considered, and P= 2T -\- W, as in equa- 
tion (1). 

Constants of the Machine. — As the constants of the 
machine are likely to change with use, they should be deter- 
mined before every important test, and the final results cor- 
rected accordingly. 



222 EXPERIMENTAL ENGINEERING. [§ *5S 

1. To determine the constant WR, swing the pendulum to 
a horizontal position, as determined by a spirit-level ; support 
it in this position by a pointed strut resting on a pair of scales. 
From the weight, corrected for weight of strut, get the value of 
WR ; this should be repeated several times, and the average 
of these products obtained. 

2. Obtain the weight of the pendulum by a number of care- 
ful weighings. 

3. Measure the length and radius of the journal ; compute 
the projected bearing-surface 2{2lr). 

WR 

4. Compute the constant , which should equal twice 

the reading of the arc showing the coefficient of friction when 
the pendulum is at an angle of 30 , since sine of 30 equal J. 

The following are special directions for obtaining the co- 
efficient of friction with the Thurston machine. 

155. Directions for obtaining Coefficient of Friction 
with* Thurston's Oil-testing Machines. — Cleaning. — In the 
testing of oils great care must be taken to prevent the mixing 
of different samples, and in changing from one oil to another 
the machine must be thoroughly cleaned by the use of alkali 
or benzine. 

In the test for coefficient of friction the loads, velocity, and 
temperature are kept constant for each run ; the oil-supply is 
sufficient to keep temperature constant, the journals being 
generally flooded. The load is changed for each run. 

The following are the special directions for the test of 
Coefficient of Friction, as followed in the Sibley College Engi- 
neering Laboratory. 

Apparatus. — Thurston's Standard Lubricant Testing-ma- 
chine; thermometer; attached speed-counter. (See Art. 151, 
page 217.) 

Method. — Remove and thoroughly clean the brasses and 
the steel sleeve or journal by the use of benzine. Put the 
sleeve on the mandrel ; place the brasses in the head of the 
pendulum and see that the pressure spring is set for zero and 
pressure as indicated by the pointer on the scale. Slide the 



§ 1 55-] FRICTION— TESTING OF LUBRICANTS. 22$ 

pendulum carefully over the sleeve, put on the washer, and 
secure it with the nut. See that the feeding apparatus is in 
running order. Belt up the machine for the high speed and 
throw on the power, at the same time supplying the oil at a 
rate calculated to maintain a free supply. By deflecting the 
pendulum and using a wrench on the nut at the bottom in- 
crease the pressure on the brasses gradually until the pointer 
indicates 50 lbs. per square inch. 

Determine the constants of the machine as explained irr 
Article 1 54, page 222; measure the projected area of journal 
bearing-surface, and the weight and moment of the pendulum. 
Ascertain the error, if any, in the graduation of the machine,, 
and correct the results obtained accordingly. 

Make a run at this pressure, and also foi pressures of 100, 
150, and 200 lbs.; but do not in general permit the maximum 
pressure in pounds per square inch to exceed 44,800 ~ (v -f- 20}. 
Begin by noting the time and the reading of the revolution- 
counter ; take readings, at intervals of one minute, of the arc 
and the temperature until both are constant. . At the end of 
the run read the revolution-counter and note the time. 

The velocity, v, in rubbing surface in feet per minute should 
be computed from the number of revolutions and circumfer- 
ence of the journal. 

Make a second series of runs, with constant pressure and 
variable speed. 

In report of the test state clearly the objects, describe 
apparatus used and method of testing. 

Tabulate data, and make record of tests on the forms given. 

Draw a series of curves on the same sheet, showing results 
of the various tests as follows : 

1. With total friction as abscissae, and pressure per square 
inch as ordinates ; for constant speed. 

2. With coefficient of friction as abscissae, and pressure per 
square inch as ordinates ; for constant speed. 

3. With coefficient of friction as abscissae, and velocity o£ 
rubbing in feet per minute as ordinates ; pressure constant. 



224 EXPERIMENTAL ENGINEERING. [§ 157- 

156. Instructions for Use of Thurston's R. R. Lubricant- 
tester. (See Article 152, page 218.) — Follow same directions 
for coefficient of friction-test as given for the standard machine, 
applying the pressure as explained in Article 155, page 222. 

Water or oil of any desired temperature can be forced 
through the hollow boxes by connecting as shown in Fig. 80, 
page 191, and the temperature of the bearings thus maintained 
at any desired point. With this arrangement the machine may 
be used for testing cylinder-stocks, as explained in directions 
for using Boult's machine (see Article 161, page 231). The con- 
cise directions are : 

1. Clean the machine. 

2. Obtain the constants of the machine ; do not trust to the 
graduations. 

3. Make run under required conditions, which may be with 
^ach rate of speed. 

a. With flooded bearings, temperature variable. 

b. With flooded bearings, temperature regulated by 

forcing oil or water through hollow brasses. 

c. Feed limited, temperature variable or temperature 

regulated. 
In all cases the object will be to ascertain the coefficient of 
friction. 

157. Riehle's Oil-testing Machine. — This machine con- 
sists of an axis revolving in two brass boxes, which maybe 
clamped more or less tightly together. The machine as shown 
in Fig. 113 has two scale-beams, — the lower one for the purpose 
of weighing the pressure put upon the journal by the hand- 
screw on the opposite side of the machine, the upper one for 
measuring the tendency of the journal to rotate. The upper 
scale-beam shows the total friction, or coefficient of friction, as 
the graduations may be arranged. A thermometer gives the 
temperature of the journal ; a counter the number of revolu- 
tions. 

Let P equal the total pressure applied to the bearings. 
Let B equal the projected area of the journal-bearings,/ equal 



§ 1 57.] FRICTION— TESTING OF LUBRICANTS. 225 

the pressure per square inch ; F equal the total friction ; / equal 




Fig. 113.— RiEHLfi's Oil-testing Machine. 



the coefficient of friction; n equal the arm of the bearing 
a the arm of the total pressure. Then do we have 



/-; 



/= 



*r. 



and 



Bfn = aP 9 






226 EXPERIMENTAL ENGINEERING. [§ 1 58. 

If / be maintained constant, and a -=- n be made the value 
of the unit of graduation on the scale-beam 



f= graduation. 

158. Durability of Lubricants.— In this case the amount 
of oil supplied is limited, and it is to be used for as long a time 
as it will continue to cover and lubricate the journal and pre- 
vent abrasion. To give satisfactory results, this requires a 
limited supply or a perfectly constant rate of feed, an even dis- 
tribution of the oil, and the restoration of any oil that is not 
used to destruction ; these difficulties are serious, and present 
methods do not give uniform results.* The method at present 
used is to consider the endurance or durability proportional to 
the time in which a limited amount, as one fourth c.c. will con- 
tinue to cover and lubricate the journal without assuming a 
pasty or gummy condition, and without giving a high coefficient 
of friction. The average of a number of runs is taken as the 
correct determination. In this test care must be taken not to 
injure the journal, and it must be put in good condition at the 
end of the run. 

The time or number of revolutions required to raise the 
temperature to a fixed point — for instance, 160 F. — is in some 
instances considered proportional to the durability. 

The Ashcroft (see Article 159, page 227) and the Boult (see 
Article 160, page 228) machines are especially designed for de- 
termining the durability of oils — from the former by noting the 
rise in temperature, from the latter by noting the change in the 
coefficient of friction. The difficulty of properly making this 
test no doubt lies in the loss of a very slight amount of oil 
from the journals, which is sufficient, however, to make the 
results very uncertain. 



*See paper by Professor Denton, Vol. XL, p. 1013, Transactions of Anr: 
can Society of Mechanical Engineers. 



§IOO.] 



FRICTION— TESTING OF LUBRICANTS. 



227 



159. Ashcroft's Oil-testing Machine. — This machine 
(Fig I i4)consists of an axle revolving in two brass boxes ; the 
pressure on the axle is regulated by the heavy overhanging 
counterpoise shown in the engraving. The tendency to rotate 
is resisted by a lever which is connected to the attached gauge. 
The gauge is graduated to show coefficient of friction. 




Fig. 114.— Ashcroft's Oil-testing Machine. 



The temperature is taken by an attached thermometer, and 
the number of revolutions by a counter, as shown in the figure. 

In this macnine the weights and levers are constant, the 
variables being the temperature and coefficient of friction. 

It is used exclusively with a limited supply of oil, the value 
of the oil being supposed to vary with the total number of 
revolutions required to raise the temperature to a given degree 
—for instance, to 160 F. 

160. Boult's Lubricant-testing Machine. -^This machine, 
designed by W. S. Boult of Liverpool, is a modification of 



228 



EXPERIMENTAL ENGINEERING. 



LI 1(50. 



the Thurston oil-tester, yet it differs in several essential feat- 
ures. A general view of the machine is shown in Fig 115, 
and a section of its boxes and the surrounding bush in Fig. 1 16, 




Fig. 115.— Boult's Lubricant-tester. 



The machine is designed to accomplish the following pur- 
poses: I. Maintaining the testing journal at any desired tem- 
perature. 2. Complete retention on the rubbing surfaces of 
the oil under test. 3. Application of suitable pressure to the 
rubbing surfaces. 4. Measurement of the friction between the 
rubbing surfaces. 



§ i6o.] 



FRICTION— TESTING OF LUBRICANTS. 



229 



To secure the complete retention of the oil, a complete bush 
with internal flanges is used instead of the brasses employed in 
other oil-testing machines. On 
the inside of the bush is an ex- 
panding journal, DD, Fig. 1 16, the 
parts of which are pressed outward 
against the surrounding bush by 
the springs E } or they may be 
drawn together by the set-screws 
B i?, compressing the springs is. A 
limited amount of oil is fed from 
a pipette or graduated cylinder 
on the journal, with the bush 
removed. This oil, it is claimed, 
will be maintained on the outer 
surface of the journal and on the 
interior surface of the metallic 
bush, so that it may be used to 
destruction. The bush is hollow, 
and can be filled with water, oil, 
or melting ice and brine. 

The oil to be tested can be FlG ii6 ^ ECTION OF BouLT , s LuBRICANTe 
maintained at any desired tern- tester. 

perature by a burner, F, which heats the liquid CC in the sur- 
rounding bush. The temperature of the journal can be read 
by a thermometer whose bulb is inserted in the liquid CC. 

The friction tends to rotate the bush ; this tendency is re- 
sisted by a lever connected by a chain to an axis carrying a 
weighted pendulum, G, Fig. 115. 

The motion of the pendulum is communicated by gearing 
to a hand, passing over a dial graduated to show the total fric- 
tion on the rubbing surfaces. 

The formulae for use of the instrument would be as follows : 
Let / equal coefficient of friction ; G the weight of the bob 
on the pendulum, R its lever arm ; a the angle made by the 
pendulum with the vertical; a the length of the connecting 
lever; c the radius of the axis to which the pendulum is 




2 30 EXPERIMENTAL ENGINEERING. |_§ 1 6 1, 

attached ; r the radius of the journal ; A the projected area of 
the journal ; Pthe total pressure on the journal. Then 

-.— Gsina =/AP, 

re J 



from which 



aGR sin a sin a 
/= rc AP ~ = ~~F~> ( constant -) 



In this instrument the total pressure P is usually constant 
and equal to 68 lbs., so that the graduations on the dial must 
be proportional to sin a. 

If the graduations are correct, the coefficient is found by 
dividing the readings of the dial by P (68 lbs.). The work of 
friction is the product of the total space travelled into the total 
friction, and this space in the Boult instrument is two thirds of 
a foot for each revolution, or two thirds of the number of 
revolutions. 

The instrument cannot be used with a constant feed of oil, 
nor can the pressures be varied except by changing the 
springs E. 

161. Directions for Durability Test of Oils with Boult's 
Oil-testing Machine. — To fill cylindrical oil-bath, take out 
the small thumb-screw in cylindrical bath and insert a bent 
funnel. Pour in oil— any sort of heavy oil maybe used — until 
it overflows from the hole in which funnel is inserted, and re- 
place thumb-screw. 

I. See that the friction surfaces are perfectly clean. These 
can be examined by tightening the set-screws in order to de- 
press the spring. This will enable the cylindrical bath to be 
lifted away. After seeing that the surfaces are perfectly clean, 
pour on a measured quantity of the lubricant to be tested, 
and reset the cylinder-bath in position. Slacken set-screws 
so as to allow the spring to have full pressure. The set-screws 
should not be removed entirely when slackening. 



§ 1 62. J FRICTION— TESTING OF LUBRICANTS. 23 I 

• 

2. Light the Bunsen burner. 

3. The thermometer indicates the temperature to which 
the lubricant has to be subjected in the steam-cylinder, being 
graduated in degrees Fahrenheit, and their equivalent in pounds 
pressure. Thus, if the working steam-pressure is 60 lbs., the 
thermometer shows that the heat of steam at that pressure is 
307 Fahr.; whilst at lOO lbs. pressure its temperature is 358 
Fahr., etc. Run the tester, say, until there is a rise of 50 per 
cent ; in some cases it is preferable to run the tester until 
there is a rise of 100 per cent of the friction first indicated. 
There does not appear to be any advantage in going beyond 
this, as the oil is then practically unfit for further use, and 
there is danger of roughening the friction surfaces. 

4. When it is considered desirable to ascertain the distance 
travelled by the friction surfaces during a test, read off the 
counting-indicator before and after the test, and subtract the 
lesser from the greater total, and the difference will represent 
the number of revolutions made during the test. As the fric- 
tion surfaces travel two thirds of a foot during each revolution, 
the number of feet travelled is arrived at by simply deducting 
from the number of revolutions made, one third thereof. 

The value of the oil is proportional to the number of feet 
travelled by the rubbing surfaces. 

The speed at which the tester should be run should be 
about five to six hundred revolutions per minute. For quick- 
speed engine-oil the speed may be increased to about a thou- 
sand per minute. 

162. Experiment with Limited Feed.— The object of this 
experiment is to ascertain the variation in the coefficient of 
friction due to a change in the rate of feed. 

The experiment is to be made with the feeding apparatus 
arranged so that the supply can be regulated. Different runs 
are made with different rates of feed, and the variation in 
the coefficient of friction determined. Fig. 1 1 1, p. 219, repre- 
sents the Thurston R. R. Lubricant-tester as arranged for the 
experiment, with a Constantly diminishing rate of feed, by Pro- 
fessor G. W. Bissel. In this case oil is obtained by the siphon 



32 



EXPERIMENTAL ENGINEERING. 



IS 162. 



M from the burette N, and conveyed by the candle-wicking P 
to a copper rod H inserted in the bearings. The rate of flow 
will depend upon the height of the oil in the burette N above 
the end of the siphon-tube M, and as the head gradually di- 
minishes from loss of oil, the rate of flow will decrease. 

The quantity of oil used is to be determined by gradua- 
tions on the burette. The increase in coefficient of friction 
due to the constantly diminishing rate of feed is shown in Fig. 
86, the coefficients of friction being shown by the dotted 
lines, corresponding to a given rate of feed and a given time 
in minutes. 




.002 
Coefficient ofJFriction 



Fig 



.006 



The experiment with head and feed maintained constant 
during each run would represent very closely the usual condi- 
tions of supplying lubricants. 

In this case, provided there was no loss of oil from the 
journals, the experiment might show — 

1. The laws of friction for ordinary lubrication. 

2. The most economical rate of feed for a given lubricant. 



§ 1630 



FRICTION— TESTING OF LUBRICANTS. 



233 



3. The value of the lubricants on the joint basis of amount 
consumed and coefficient of friction. 

A few tables showing coefficients of friction which has been 
obtained in various trials are given in the Appendix for refer- 
ence. 

163. Forms for Report. — The following are the forms used 
in Sibley College for data and results of lubricant test: 



REPORT OF LUBRICANT TEST. 

Name of Lubricant 

Mark...* Lab. No Date 

Source Observer. . 

Investigation 



No. of test 

Pressure on journal, lbs. per sq. inch... 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g 

Average coefficient of friction , 

Minimum coefficient of friction. , 

No. of revolutions 

No. of feet travelled by rubbing surface, 
Elevation of temperature 



Time. 
Min- 
utes. 



Total 
Revolu- 
tions. 



Temper- 
ature. 



Read- 
ing on 
Arc. 



Coeffi- 
cient of 
Friction. 



Time. 
Min- 
utes. 



Total 
Revolu- 
tions. 



Temper- 
ature. 



Read- 
ing on 
Arc. 



Coeffi- 
cient of 
Friction. 



VISCOSITY AND RESULTS OF OIL TEST. 



Kind of oil Date.. 189.... 

Received from... 

Color. Ash % 

Specific gravity ° B. Tar % 

" " waterioo. Chill-pt • F. 

Flashing pt ° F. Loss at ° F. for 3 hrs % 

Burning-pt ° F. Acid 



2 34 



EXPERIMENTAL ENGINEERING, 
VISCOSITY TEST. 



[§ 163. 



No. 


Time of Flow of 100 c.c. in Seconds. 


Temperature 
Degrees F. 


Lubricating 

Value Lard-oil 

100. 


Sample. 


Lard-oil. 


Water. 


I 












2 












a 












A 












C 
























RESULTS OF FRICTION TEST. 



Date. 



189 . 



Highest reading 

Lowest reading 

Average reading 

Drops per min 

Time of run, min. . . . 
Speed: 

Rev. per min 

Miles per hour.. . . 
Pressure: 

Total lbs 

Per sq. in., lbs. 

Coefficient of friction. 



Temp. Arc 



II. 



Temp. Arc 



III. 



Temp. Arc 



Average. 



TEST FOR RESINS. 

Flow on plane inclined degrees. 

Kind of plane Tempt, room. 

Time in hrs., Sample , Lard-oil , Water. 



CHAPTER VII* 

MEASUREMENT OF POWER— DYNAMOMETERS— BELT- 
TESTING MACHINES. 

164, Classes. — Dynamometers are instruments for measur- 
ing power. They are of two classes : 1. Absorption; 2. Trans- 
mission. In the first class the work received is transformed 
by friction into heat and dissipated ; in the second class the 
dynamometer absorbs only so much force as is necessary to 
overcome its own friction, the remainder being transmitted. 

165. Absorption Dynamometer.— The Prony Brake.* — 
The Prony brake is the most common form of absorption dy- 
namometer. This brake is so constructed as to absorb the 
work done by the machine in friction, this friction being pro- 
duced by some kind of a surface connected to a stationary 
part, and which rubs on the revolving surface of the wheel 
with which it is used. The brake usually consists of a por- 
tion which can be clamped on to a wheel (see Fig. n 8, page 
2 39), with more or less pressure, and an arm or its equivalent. 
The part exerting pressure on the wheel is termed the brake- 
strap ; the perpendicular distance from the line of action of 
the weight, G, to the centre of the wheel is termed the arm of 
the brake. The brake is prevented from turning by a definite 
load which we term G, applied at a distance equal to the 
length of the arm (a) from centre of motion. The work of 
resistance would then evidently be equal to the product of the 
weight of resistance, G, into the distance it would pass through 



*See Engine and Boiler Trials, by R. H. Thurston, page 157; Mechanics of 
Materials, by I. P. Church, page 269; Du Bois' Weisbach's Mechanics of En- 
gineering, page 13. 

235 



236 • EXPERIMENTAL ENGINEERING. [§ 1 67, 

if free to move. If n be the number of revolutions per minute, 
the horse-power shown by the brake would evidently be 

2nGan -r- 33000. ....... (1) 

Brakes are made with various rubbing surfaces, and with 
various devices to maintain a constant resistance. 

166. Stresses on the Brake-strap. — Formula. — The 
strains on the brake-strap are essentially the same as those 
on a belt, as given in Article 128, page 199. 

That is, if T x represent the greatest tension, T 2 the least 
tension, c the percentage that the arc of contact bears to the 
■whole circumference, N the normal pressure, F the resistance 
of the brake, f coefficient of friction, 

T t -T n = Fi N = F+f; 

T 

—L = iqwWc— Number whose log is 2.7288/*: = B 



T ' = B^ (3) 



167. Designing a Brake.* — The actual process of designing 
a brake is as follows : There is given the power to be absorbed, 
number of revolutions, diameter and face of the brake-wheel. 
In case a special brake-wheel is to be designed, the area of 
bearing surface is to be taken so that the number obtained by 
multiplying the width w of the brake in inches by the velocity 
of the periphery v of the wheel in feet per minute, divided by 



*See " Engine and Boiler Trials," by R. H. Thurston, pages 260 to 282; 
also, " Friction and Lubrication." 






§167.] MEASUREMENT OF POWER. 237 

the horse-power H> shall not exceed 500 to 1000.* Call this 
result K. Then 

„, WV 

K= w . 



400 to 500 is considered a good average value of K. 

The value of the coefficient of friction f should be taken 
as the lowest value for the surfaces in contact (see table of co- 
efficient of friction in Appendix). This coefficient is about 0.2 
for wood or leather on metal, and about 0.15 for metal on metal.. 

Let H be the work to be transmitted in horse-power, ;z the 
number of revolutions of the brake-wheel, D its diamete*-- 
then the resistance F of the brake must be 



p __ 33000^ f 



The arc of contact is known or assumed, and may be expressed 
as convenient (see Article 128) in circular measure 0, degrees 
a, or in percentage of the whole circumference c. 

Example. — Assume the arc of contact as 189 degrees 
(c =0.5), the diameter of brake-wheel 4 feet, coefficient or 
friction (/*=o.i5), face of brake-wheel 10 inches, revolutions 
90, horse-power 70. Find the safe dimensions of the brake- 
strap and working parts of the brake. 

Then, from page 236, 

B = icf^m = jo ** 6 . 
That is, B equals the number whose logarithm is 0.2046 ; or, 

B = 1.602. 

*See also " Engine and Boiler Trials," by R. H. Thurston, pp. 272 and 270^ 



238 EXPERIMENTAL ENGINEERING. [§ 1 67. 

Thus if the brake-wheel is 4 feet diameter revolving at 90 
revolutions per minute : from equation (4) 

(33000^(70) = 

(*)(4)( 9 o) 2 °43P°«nas. 



Taking B as above, and substituting in equations (2) and (3). 
we have 



- 20 « fig) = 5436; 



A% .602 3395, 



^=52*3 = 13620. 
.15 



From the value of T, , the maximum tension, we compute the 
required area of the brake-straps, using 10,000 pounds as the 
safe-working strain. 

Section of brake-straps = 5436 -r- 10000 = 0.55 square inch. 
The assumed width of brake-wheel is 10 inches ; this gives 
for the value of K, by equation page 237. 

K = (10) (1 132) -T- 70 = 162 ; a low value. 

If it is proposed in this brake to use 3 straps, each 2 inches 
wide, the thickness will then be 

0.55 -r- 6 = 0.091 inch. 

To determine a convenient length of the brake-arm, con- 
sider equation (1) for work deliyered in horse-power. 

H = 2nGan -7- 33000. 



§ 169.] MEASUREMENT OF PQWER. 239 

By dividing both terms by 27t, 

H '= Gan ~ 5252; 

£_5252 
H an 

168. Brake Horse-power. — The following table will often 
be convenient for determining the delivered horse-power from 
a brake. 

HORSE-POWER PER 100 REVOLUTIONS FROM A BRAKE. 



Length of Brake-arm, 


Factor to multiply 


Ratio of scale-read- 


feet. 


scale-reading to give 


ing to horse- power, 




horse-power, H-r~ G. 


G^-H. 


I 


O.OI9 


52.52 


2 


.038 


26.26 


3 


.057 


17.51 


4 


.076 


13-13 


5 


.090 


IO.5O 


5.252 


.IOO 


IO.OO 


6 


.114 


8.75 


7 


.133 


7-50 


8 


.1*2 


6.56 


9 


.172 


5.83 


10.504 


.200 


5.00 



169. Different Forms of Prony Brakes. — Various forms 
of brakes are made. Fig. 118 shows a very simple form of 



TC 




Fig. 118. — Prony Brake. 



Prony brake, in which the rubbing surfaces are made by two 
wooden beams clamped together by the bolts C C. Weight is 
applied to the arm E at the point G ; the stops D D prevent a 
great range of motion of the arm ; the projection F is used to 
hang on sufficient counterbalance to prevent the brake from 



240 



EXPERIMENTAL ENGINEERING. 



[§ I7a 



revolving by its own arm-weight when the screws C C are very- 
loose. The net load acting on the brake-arm is the difference 
between the weight at G and that at F, reduced to an equiva- 
lent weight acting at G. 

Brakes are usually constructed by fastening blocks of wood, 
on the inside of flexible bands of iron, so as to encircle a 
wheel. The inside of the blocks should be fitted to the wheel, 
and the spaces between the blocks should be at least equal to 
one third the area of the block. The iron bands are connected 
to the brake-arm in such a manner that the tension on the 
wheel can readily be changed. The form of such a brake is 
shown in Fig. 119 attached to a portable engine. 




Fig. 119*— Brake applied to Portable Engine. 

170. Strap-brakes. — Brakes are sometimes made by taking 
one or more turns of a rope or strap around a wheel, as shown 




Fig. 120.— Strap-brake. 



in Fig. 120. In this case weights must be hung on both sides, 
and since the arm of action is equal, the resultant force 



§ I73-] MEASUREMENT OF POWER. 24 1 

acting is the difference between the two weights : that is, in 
the figure the resultant force \s A — B ; the equivalent space 
passed through is the distance travelled by any point of the 
circumference of the wheel in a given time. The work done 
is the product of these quantities. 

171. Self-regulating Brakes. — Brakes with automatic 
regulating devices are often made ; in this case the direction of 
motion of the wheel must be such as to lift the brake-arm. If 
the tension is too great the brake-arm rises a short distance, 
and this motion is made to operate a regulating device of some 
sort, lessening the tension on the brake- ^ 

wheel ; if the tension is not great enough, ^=jjk k b l 

the brake-beam falls, producing the oppo- ^fipf£\ j | f 

site effect. V\V ! I i 

172. Brake with oblique Arm. — A v%N \ 
very simple form of self -regulating brake \'^?M = 
is shown in Fig. 121: in this case the \ pJ, ;E 
arm is maintained at an angle with the ^••'' A 
horizontal. If the friction becomes too JL 
great, the weight G rises, and the arm of w 
the brake swings from A to E. thus in- ™ - „ , ^ 

<=» ' Fig. 121.— Self-regulating 

creasing the lever-arm from BC to LC; if Brake. 

the friction diminishes, the lever-arm is correspondingly dimin- 
ished, thus tending to maintain the brake in equilibrium. 

173. Alden Brake. — The Alden brake (see Figs. 122 to 12 5) 
is an absorption dynamometer in which the rubbing surfaces 
are separated by a film of oil, and the heat is absorbed by 
water under pressure, which produces the friction. It is con- 
structed by fastening a disk of cast-iron, A, Fig. 122, to the 
power-shaft ; this disk revolves between two sheets of thin 
copper E E joined at their outer edges, from which it is sepa- 
rated by a bath of oil. Outside the copper sheets on either 
side is a chamber which is connected with the water-supply at 
G. The water is received at G and discharged at H, thus main- 
taining a moderate temperature. Any pressure in the chamber 
causes the copper disks to press against the revolving plate, pro= 
ducing friction which tends to turn the copper disks. As these 



242 



EXPERIMENTAL ENGINEERING. 



[§ 174. 



are rigidly connected to the outside cast-iron casing and brake, 
arm P, the turning effect can be balanced and measured the 
same as in the ordinary Prony brake. The pressure of water 
is automatically regulated by a valve V, Fig. 125, which is par- 




ZETS 



s fsl 



Fig. 124. — Section. 



Fig. 123. — Alden's Brake 



Fig. 122. — Section. 




Fig. 125.— Valve. 

tially closed if the brake-arm rises above the horizontal, and is 
partially opened if it falls below ; this brake with a constant 
head gives exceedingly close regulation. 

174. Hydraulic Friction-brake. — The author has designed 
a hydraulic friction-brake that can be applied to the surface 
of an ordinary brake-wheel. The brake consists of a tube of 
copper with an oval or rectangular cross-section, which very 
nearly encircles the brake-wheel, and has both ends closed. 
The greatest dimension in its cross-section is equal to the 
width of the brake-wheel, and its least dimension is one half to 
three fourths of an inch. One end of the tube is connected 
with the water-supply, the other to the discharge, which can 
be throttled as required. Outside is a band of iron completely 
encircling the tube and the brake-wheel, and held rigidly to- 
gether by means of bolts. To this band is fastened the brake- 
arm, and also one end of the copper tube. When water-pres- 



§ 176.] MEASUREMENT OF POWER. 243 

sure is applied to the tube, it tends to assume a round cross- 
section, the shorter diameter increasing and the greater 
diameter diminishing. As these changes cannot take plact 
because of the outer band of iron, pressure is exerted on the 
surface of the brake-wheel, and motion of the brake-wheel 
tends to revolve the tube and band of iron. This is resisted 
by the weight on the arm of the brake. The water-pressure is 
regulated automatically by a slight motion of the brake-arm, 
which closes or opens the supply-valve as is required. The 
arm may be permitted to act downward on a pair of scales, by 
interposing a spring of the requisite stiffness between it and 
the platform of the scales. To prevent wear of the copper 
tube thin sheets of iron may be interposed. A lubricant is 
applied by means of lubricators fixed near the ends of the 
tube. 

175. Removal of the Heat generated by the Brake. — 
Various devices have been adopted to secure the removal of 
the heat. One method is to cast the outer rim of the brake- 
wheel hollow, and connect this by a tube with a cavity in the 
centre of the axis, so that water can be received at one end of 
the axis and discharged at the other. Another way is to leave 
a deep internal flange on the brake-wheel, and in using the 
brake, to supply water by means of a crooked pipe on one side 
and to scoop it out by a pipe with a funnel-shaped mouth bent 
to meet the current of water near the opposite side of the 
wheel. Water is sometimes run on to the surface through a 
hose, but aside from the inconvenience due to flying water, 
if anv of the rubbing surfaces are of wood it is likely to make 
sudden and irregular variations in the coefficient of friction 
that are difficult to control. 

176. Applying Load. — In applying the load, care must be 
taken that its direction is tangent to the circle that would be 
described by the brake-arm were it free to move. In other 
words, the virtual brake-arm must be considered as perpendic- 
ular to this force. If a vertical load or weight is applied, the 
brake-arm must be horizontal, and equal in length to the dis- 
tance from this vertical line to the centre of the motion. 



244 EXPERIMENTAL ENGINEERING. [§ 1 78. 

It will be found in general safer and more satisfactory to 
have the motion of the brake-wheel such as to produce a 
downward force, which may be measured by a pair of scales, 
rather than the reverse, which requires a weight to be sus- 
pended on the brake-arm. There should be a knife-edge 
between the brake-arm and the load ; in case of downward 
motion, the support upon the scales, should be made the proper 
length to hold the brake-arm horizontal. 

177. Constants of Brake. — All brakes with unbalanced 
arms have a tendency to turn, due to weight of the arm. 
This amount must be ascertained and added to or taken from 
the scale or load readings as required by the rotation, in order 
to give the correct load. To ascertain this amount, the brake 
may be balanced on a knife-edge, with a bearing point directly 
over the centre of the wheel, and the correction to the weight 
obtained by readings on the scale. It is obtained more accu- 
rately by making the brake loose enough to move easily on the 
wheel ; then apply a spring-balance at the end of the arm ; first 
pull the arm upward through an arc of about 3 either side of 
-its central position, moving it very slowly and gradually: the 
reading will be the weight plus the friction. Then let it back 
through the same arc very slowly and gradually, and the read- 
ing will be the weight less the friction. The sum of these two 
results will be twice the correction for the brake-arm. Repeat 
this three times for an average result. In case the friction is 
greater than the weight this second result will be negative, but 
the method will remain the same. 

The weight of the brake, as generally mounted, is carried 
on the main bearings of the wheel, from which the power is 
obtained, and virtually increases its weight. This may in some 
instances increase perceptibly the friction of the journals of 
the wheel, but is generally an imperceptible amount. This 
weight can be reduced when desired, by a counterbalance con- 
nected to the brake by means of guide-pulleys. 

178. Directions for Using the Prony Brake.— i. See 
that the brake-wheel is rigidly fastened to the main shaft. 
2. Provide ample means of lubrication. 



§ l8o.j MEASUREMENT OF POWER. 245 

3. If the brake-wheel has an internal rim, provide means 
for supplying and removing water from this rim. 

4. Find the equivalent weight of brake-arm to be taken 
from or added to the load, depending on the direction of 
motion of the wheel. 

5. In applying the load, tighten the brake-strap very I 
slowly, and give time for the friction to become constant >e« ; 
fore noting readings of the result. 

6. Note the time, number of revolutions, length of brake- 
arm, corresponding load, and calculate the results. 

179. Pump Brakes. — A rotary pump which delivers water 
through an orifice that can be throttled or enlarged at will, has 
been used with success for absorbing power. 

If the casing of the pump is mounted so as to be free to 
revolve, it can be held stationary by a weighted arm, and the 
absorbed power measured, as in the case of the Prony brake. 
If the casing of the pump is stationary, the work done can be 
measured by the weight of water discharged multiplied by the 
height due to the greatest velocity of its particles multiplied 
by a coefficient to be determined by trial.* 

A special form of the pump-brake, with casing mounted so 
that it is free to revolve, has been used with success on the 
Owens College experimental engine by Osborne Reynolds. 
In this case the brake is practically an inverted turbine, the 
wheel delivering water to the guides so as to produce the 
maximum resistance. The water forced through the guides 
at one point is discharged so as to oppose the motion Df the 
wheel at anothe; point. 

180. Fan-brakes^— A fan or wheel with vanes revolved in 
water, oil, or air will absorb work, and in many instances forms 
a valuable absorption-dynamometer. 

The resistance to be obtained from a fan-brake is expressed 
by the formula f 

IT 
Rl=lKDA—> 

• ^ 

* See Rankine, Machinery and Mill-work, page 404. 
\ Ibid., page 406. 



246 



EXPERIMENTAL ENGINEERING, 



in which ^/equals the moment 
of resistance, V the velocity in 
feet per second of the centre 
of vane, A the area of the vane 
in square feet. / equals the 
distance from centre of vane 
to axis in feet, D the weight 
per cubic foot, of fluid in which 
the vane moves, K a coefficient, 
found by experiment by Pon- 
celet to have the value 




iST =1.254+ l _ s , 



n which s is the distance in 

feet from the centre of the 

entire vane to the centre of 

:hat half nearest the axis. 

vVhen set at an angle i with 

the direction of motion the 

value for Rl must be multi- 

2 sin 2 i 
plied by — ; — r-7-. . 
r 1 + sin 1 

181. Traction-dynamome- 
ters. — Dynamometers for sim- 
ple traction or pulling are 
usually constructed as in Fig. 
126. Stress is applied at the 
two ends of the spring, which 
rotates a hand in proportion 
to the force exerted. 








en ( 


I 

, il 


/ > 

/ Q 
O 
55 


T 
tu 

« III u 
o° 


Q 


a 

K 

O 

O 


111 W 

ti\\ <$> INC 


2. 
O 


! 1 H 

ydxL J 






-RE 

M 


(S-~- 




PS 






| 


~^-~- ""'--iJJ II 






; 1 _ 




a 

6 

l 






\ i 


wl 



Fig. 146. — Dynamometer for Traction. 



§ 183.] MEASUREMENT OF POWER. 2.47 

Recording Traction-dynamometers. — These are constructed 
in various forms. Fig. 127 shows a simple form of a recording 
traction-dynamometer, designed by C. M. Giddings. Paper is 
placed on the reel A, which is operated by clock-work; a 
pencil is connected at K to the band, and this draws a diagram, 
as shown in Fig. 128, the ordinates of which represent pounds 



Tbsr 



Fig. 128.— Diagram from Traction-dynamometer. 



of pull, the abscissae the time. The drum may be arranged 
to be operated by a wheel in contact with the ground : then the 
abscissa will be proportional to the space, and the area of the 
diagram will represent work done. 

182. General Types of Transmission-dynamometers.* 
— Transmission-dynamometers are of different types, the ob- 
ject in each case being to measure the power which is 
received without absorbing any greater portion than is neces- 
sary to move the dynamometer. They all consist of a set of 
pulleys or gear-wheels, so arranged that they may be placed 
between the prime movers and machinery to be driven, while 
the power that is transmitted is generally measured by the 
flexure of springs or by the tendency to rotate a set of gears, 
which may be resisted by a lever. 

183. Morin's Rotation-dynamometer. — In Morin's dy- 
namometer, which is shown in Fig. 129, the power is trans- 
mitted through springs, FG, which are thereby flexed an 
amount proportional to the power. The flexure of the springs 
is recorded on paper by a pencil z fastened to the rim of the 

* See Thurston's Engine and Boiler Trials, page 264 ; also Weisbach'9 
Mechanics, Vol. II., pages 39-73 ; also Rankine's Steam-engine, page 42. 






248 



EXPERIMENTAL ENGINEERING. 



L§ i»a 



wheel. A second pencil is stationary with reference to the 
frame carrying the paper. The paper is made to pass under 
the pencil by means of clock-work driven by the shafting, 
which can be engaged or disengaged at any instant by operating 
the lever R. The springs are fastened at one end rigidly to 
the main axle, which is in communication with the prime 
mover, and at the other end to the rim of the pulley, which 
otherwise is free to turn on the main shaft. The power is 
taken from this last pulley, and this force acts to bend the 




Fig. 129. — Morin Rotation-dynamometers. 



springs as already described. In the figure A is a loose pulley 
B is fixed to the shaft 

The autographic recording apparatus of the Morin dyna- 
mometer consists essentially of a drum, which is rotated by 
means of a worm-gear, UK > cut on a sleeve, which is concentric 
with the main axis. This sleeve slides longitudinally on the 
axis, and may be engaged with or disengaged from the frame at 
any instant by means of a lever. When this sleeve is engaged 
with the frame and made stationary the recording apparatus 
is put in motion by the concentric motion of the gearing, SV, 
with respect to the axis. The pencil attached to the spring 
will at this instant trace a diagram on the paper whose ordi- 



§ 184.] MEASUREMENT OE POWER. 249 

nates are proportional to the force transmitted. The rate of 
rotation of the drums carrying the paper, with respect to the 
main axis, is determined in the same manner as though the 
gears were at rest — by finding the ratios of the radii of the 
respective wheels. Thus the amount of paper which passes 
off from one drum on to the other can be proportioned to the 
space passed through, so that the area of the diagram may be 
proportional to the work transmitted. 

To find the value of the ordinates in pounds the dyna- 
mometer must be calibrated ; this may be done by a dead pull 
of a given weight against the springs, thus obtaining the 
deflections for a given force ; or, better, conneGt a Prony brake 
directly to the rim of the fixed pulley B, and make a series of 
runs with different loads on the brake, and find the correspond, 
ing values of the ordinates of the card. 

184. Calibration of the Morin Dynamometer. — Appara- 
tus. — Speed-indicator, dynamometer-paper, and Prony brake. 

1. Fasten paper on the receiving drum, wind off enough 
to pass over the recording drum, and fasten the end securely 
to the winding drum. See that the gears for the autographic 
apparatus are in perfect order, and that both pencils give 
legible lines. Adjust the pencil fixed to the frame of the 
clock-work, so that it will draw the same line as the movable 
pencil, when no load is applied. 

2. With the apparatus out of gear apply the power. Take 
a card with no load. This card will be the friction work of 
the dynamometer. 

3. Apply power and load, take cards at intervals: these 
cards will represent the total work done. This, less the fric- 
tion work, will be the power transmitted. The line traced 
by the pencil affixed to the frame of the clock-work must in 
all cases be considered the zero-line, or line of no work. 

4. To calibrate the dynamometer, attach a Prony brake to 
the same shaft and absorb the work transmitted. This trans- 
mitted work must equal that shown by the Prony brake. 
Find constants of brake as explained Article 177, page 211. 

5. Draw a calibration-curve, with pounds on a brake-arm, 



250 



EXPERIMENTAL ENGINEERING. 



[§ 186. 



reduced to an equivalent amount acting at a distance equal to 
the radius of the driving-pulley of the dynamometer, as 
abscissae, and with ordinate of the diagram as ordinate. 
Work up the equation of this curve. 

6. In report of calibration make record of time, number of 
revolutions brake-arm, equivalent brake-load for arm equal to 
radius of dynamometer-pulley, length of ordinate, scale of 
ordinate. Describe the apparatus. 

7. In using it, insert it between the prime mover and re. 
sistance to be measured. Determine the power transmitted 
from the calibration. 

185. Form of Report— The following form is useful in 
calibrating this dynamometer : 



CALIBRATION OF MORIN DYNAMOMETER. 

Kind of brake used • Length of brake-arm 

Weight of brake-arm lbs. Zero-reading of scales. . . . 

Radius of driving-pulley ft. Observers 



..ft. 

.lbs. 



Date. 



189. 



No. 



Resolutions per Minute. 



Up. Down, Mean 



Effective 

Brake-load 

lbs. 



Equivalent 
Load on 
Driving- 
pulley, lbs. 



Ordinate, Inches. 



Up. Down. Mean 



Brake 
H. P. 



Remarks: 



Equation of Curve, 
...... K- , 



186. Steelyard-dynamometer. — In this dynamornetei the 
pressure of the axle of a revolving shaft is determined by 
shifting the weight G on the graduated scale-beam AC. 

The power is applied at P, putting in motion the train of 
gear-wheels, and is delivered at Q. 

Denote the applied force by P, the delivered force by Q, 



1 86.] 



MEASUREMENT OF POWER. 



25 



the radius KM by a, KE by r, LF by r x , NL by b % the force 
delivered at E by R t that at F by R t . 
We shall have 

Rr = Pa, also Rf^Qb. 

But 

R(ED) = R % {FD)\ 

and since is/> = F27, 

R = R t . 

The resultant force Z == R -f- tf, = 2R. 
.:R = iZ-, P=iZr + a; Q = \Zr x ±*. 

If we know the number of revolutions, the space passed 
through by each force can be readily calculated, and the work 
found by taking the product of the force into the space 
passed through. 

JL c 




Fig. 130. — Hachette's Steelyard-dynamometer. 

Consideration of Friction.— The friction of the axle and 
gear-teeth will increase the force R and decrease the force R r 
Let pi be the experimental coefficient expressing this friction. 
Then 

P=i(i+»)Zr + a; 
Q^Hi-^Zr^t; 
Par, — Qbr 



M = 



Par, + Qbr 



252 



EXPERIMENTAL ENGINEERING. 



[§ 188 




Fig. 131.— Pillow-block Dyna 

MOMETER. 



187. Pillow-block Dynamometer. — The pillow-block dy. 
namometer operates on the same principle as the steelyard 

dynamometer, but no intermediate 
wheel is used. This dynamometer, 
shown in Fig. 131, consists of the 
fixed shaft L, which is rotated by 
the power Q applied at N. The 
power rotates the gear-wheel EL, 
which communicates motion to the 
wheel KE on the same shaft with 
the wheel KM. This shaft is sup 
ported on a pair of weighing-scales so that the downward force 
Z acting on the bearing can be weighed. Let P equal the 
force delivered, let a equal the angle this force makes with the 
horizontal, let KM equal a and KE equal r , G equal the weight 
of shaft and wheel. The weight on the pillow-block at K 
must be 

Z = G + P sin a +^P = G + p(sin a + ^\ 

From which 

Z-G 



P = 



sin a -\ 

r 



When the belt is horizontal. 



tf«0 and P = {Z-G)-. 

188. The Lewis Dynamometer.* — This transmission-dy 
namometer is a modified form of the pillow-block dyna- 
mometer, arranged in such a manner that the friction of the 
gearing or journals will not affect the reading on the weighing- 
scales. This dynamometer is shown in Fig. 1 32 , and also in Fig. 
139, Article 195, page 265. The dynamometer consists of two 



*See Vol. VII., page 276, Trans. Am. Society Mechanical Engineers. 



88.] 



MEASUREMENT OF POWER. 



253 



^ear-wheels A and C, whose pitch-circles are tangent at B; 
the gear-wheel A is carried by the fixed frame T, the wheel C is 
carried on the lever BD : the lever BD is connected to the 
flxed frame T by a thin steel fulcrum, as used in the Emery 
Testing-machines (Article 67, page 105). The point D, the 
centre of wheel C, and the fulcrum are in the same right line. 
The fulcrum B permits vertical motion only of the point D. 
The point D rests on a pillar, which in turn is supported by 
a pair of scales. The shaft leading from the wheel C is fur- 
nished with a universal joint (see Fig. 139), so that its weight 
does not affect that on the journal C. In Fig. 132, A is the 




Fig. 132.— The Lewis Dynamometer. 

driving and C the driven wheel, the force to be measured being 
received on a pulley on the shaft a } transmitted through the 
dynamometer, and delivered from a pulley on the shaft c. 
From this construction it follows, that no matter how great 
the friction on the journals of the shaft c, there will be no 
pressure at the point D except what results from torsio» 
of the shaft c. This will be readily seen by considering: 

1. That any downward force acting at B will be resisted by 
the fixed frame T, and will not increase the pressure at D. 

2. A downward force acting on the lever between B and D 
will produce a pressure proportional to its distance from B. 

3. If the driven wheel C were firmly clamped to its frame, no 
force acting at B would change the pressure at D ; and since 



254 EXPERIMENTAL ENGINEERING. |J l88 - 

journal-friction would have the effect of partially clamping the 
wheel to the journal c, it would have no effect on the scale- 
reading at D. 

Denote the transmitted torsional force by Z\ the radius of 
the driven pulley by r ; the length of lever BD by a ; the scale- 
reading at D by W. Then from equality of moments 

r 

The effective lever-arm BD is to be obtained experimen- 
tally as follows : Disconnect the universal joint, shown in Fig. 
108, so as to leave the wheel C, free to turn ; block the driving- 
pulley A ; fasten a horizontal arm, ef (dotted lines, Fig. 101), 
to the shaft c, parallel to the line DB and carrying a weight 
G ; balance the scales in this position, then move the weight 
out on the lever, until the reading of the scales is increased an 
amount equal to the weight moved. The distance moved by 
the weight will equal length of the lever DB. 

Thus let ef, shown in dotted lines, represent the lever 
clamped to the axis c ; let e represent the first position of the 
weight G, and /the second position; let J^and W represent 
the corresponding scale-readings, after balancing scales without 
G on the lever, ef. 

Then we have 



Hence 



W - U DB 1 
W+G=W' = G { ^-. 



c _ W' - W __ c (f B-eB) __ c ef 



DB " DB ~'DB' 

Then will 

DB = ef. 



§ 189.] MEASUREMENT OF POWER. 255 

189. The Differential Dynamometer. — This is often 
called the Bachelder, Francis, or Webber dynamometer ; was 
invented by Samuel White, of England, in 1780, and brought 
to this country by Mr. Bachelder in 1836. 

The dynamometer portion consists of four bevel-gears, 
shown in plan in Fig, 133. 

Power is applied to the pulley M, which carries the bevel- 
x 




Fig. 133.— The Differential Dynamometer. 

wheel EE X ; the resistance is overcome by the pulley N, which 
carries the bevel- wheel FF X . Both wheels run loosely upon 
the fixed shaft XX X , and are connected by the wheels island 
E X F X . By the action of the force P and the resistance Q, the 
pressure of the wheels EE X and FF X is downward at E and F, 
and upward at E 1 and F x , tending to swing the lever GG X 
around the axis XX X , one half as fast as the pulley M. The 
weight which holds the lever-arm stationary, multiplied by the 
space it would pass through if free to move, is the measure of 
the work of the force P. A dashpot is usually attached to the 
lever GG X at G x , to lessen vibrations and act as a counterbal- 
ance. Let Z equal the vertical force acting at B and B x ; R, 
the vertical pressure between the teeth at each point of con^ 
tact ; b, the distance of B and B x from the centre C; a, the 
distance, AC, to the weight. 
. Then we have evidently 

2Z = ^R, or Z=2R\ 
also 

Ga = 2Zb = 4Rfr. 



256 



EXPERIMENTAL ENGINEERING. 



[§ I90* 



If a! is the radius of the driving-pulley M, and r the radius 
of each bevel-gear, 

r> / r> r> 2Rr G r a 

Pa' = 2Rr, or P— — r = — - -„ 

a' 2 b a! 



If friction is considered, 



P=(i+M) 



G r a 

~2 ~b a'' 



The mechanical work received is equal to P multiplied by 
the space passed through in the given time. 

This instrument has been improved by Mr. S. Webber, as 
shown in Fig. 134. 




Fig. 134. — The Webber Dynamometer. 

These dynamometers are used in substantially the same 
way as the Morin dynamometers. 

190. Calibration of the Differential Dynamometer. — 

1. See that it is well oiled, in good condition, its axis horizon- 
tal, and also that the weighing arm is horizontal for no load. 

2. Observe constants of the apparatus ; obtain weight of 
small poise* of large poise; of amount to balance beam W e . 
Measure the arm of each, and calculate the foot-pounds per 
100 revolutions corresponding to weights and graduations. 



§ I90.] MEASUREMENT OF POWER. 2$? 

3. Make a preliminary run without load, and note the 
reading of the poise required to balance the arm. This will 
determine the friction of the dynamometer without load. 
Determine the length of the arm, and the value of each sub- 
division in foot-pounds. 

4. Attach a strap-brake (see Art. 169, p. 239) to the delivery 
pulley of the dynamometer, and absorb all the force trans- 
mitted. Make a series of ten runs, each ten minutes in length, 
and during each of which the load on the Prony brake-arm is 
kept as constant as possible, but which is increased by equal 
increments, in the different runs. Take observations each 
minute during the run. 

5. The difference between the work absorbed by the brake 
and that shown by the dynamometer should be carefully de- 
termined. It is the error of the dynamometer. 

6. Note whether this error is a constant quantity, or is a 
percentage of the work delivered. 

7. In your report, describe the apparatus, give the results 
of the calibration, and draw a curve, using brake foot-pounds 
as ordinates, and dynamometer foot-pounds as abscissae. 

8. To use the dynamometer insert it between the prime 
mover and the machinery to be run. 

Special Directions for Calibrating the Webber Differential 

Dynamometer, 
Apparatus required : 

I. Ten small tension-weights. 2. Spring-balance or plat« 
form-scales. 3. Measuring-scale. 4. Calipers. 5. Stop-watch. 
Measurements : 

a. Weight of small tension-weights, 

b. " " fixed poise-weights. 

c. " " dynamometer-arm. 

d. ° " sliding poise. 

e. Length of dynamometer-arm to fixed poise. 
/. Length of dynamometer-arm to sliding poise. 
g. Diameter of brake-pulley. 

k. Thickness of brake-strap. 






2 5 8 



EXPERIMENTAL ENGINEERING. 



[§ 191 



I. Friction-run. — Remove brake. Find time, in seconds, 
of 1000 revolutions (10 rings of bell). Balance dynamometer, 
arm ; the reading is the " zero-reading" by the beam, and must 
be corrected to get the true friction-reading. 

II. Test-runs. — Put on brake ; hang one weight on its 
slack side. Time, 1000 revs. Read simultaneously dynamom- 
eter-arm and platform scales. Repeat the same with succes- 
sive weights added. 

III. To Weigh Dynamometer-arm. — Run by hand, first for- 
ward and then backward, weighing in each case the turning 
effect, with the platform-scale applied at the knife-edge of the 
dynamometer-arm, and sliding-poise set at the zero-mark. 

191. Form of Report.— The following blank is used in the 
exercises with the differential dynamometer in Sibley College: 

MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNI- 
VERSITY. 

Calibration of Differential Dynamometer. 

Kind of Brake used 

Length of Brake-arm ft. Weight of Brake-arm lbs. 

Zero-reading of Brake-scales lbs. 

Date.* .189. . Observers 





09 

§ 

1- 

« 


O <u 
H C/J 

s 


Brake-tensions, Lbs. 


Work in ft.-lbs. per ioo Revolutions. 


u 





6 ■ 
•a 

I 





3 
•J 


S3 


Dynamometer-read in gs. 


8 . 

XI 

O 


SI 

u 


a 


1 


Sgd 

Jr. *& 


Calculated 

from 

Machine 

Constants. 


T3 >,<" 

•- G II 

fi fl 
a! en rt 


V 

CO 



a 

u 
M 

2 

PQ 


£ 


T\ 


T* 


Ti-T* 


w d 


w c 


w^-w. 


»"4 


wt-w 


D.H.P. 


I 






















2 






















3 

4 
5 
6 


















































































7 
8 










































9 
IO 

































































§ I93J 



MEASUREMENT OF POWER. 
CONSTANTS OF MACHINE. 



259 





Moment Arm ft. 


Data for Beam. 


Sliding Poise, 
Weight.... lbs. 


Loads at Knife-edge. 


Weight, 
lbs. 


Value, ft.- 
lbs. per 
100 Revs. 


Moment 
Arm, 
Feet. 


Value, ft.. 
lbs. per 
100 Revs. 








First Notch 












Last Notch 






Dvnamometer-beam 




...= JV e 


Increase per Notch. 






W*= Zero-reading b 


y Beam. . 


..ft.-lbs. 


Wq-\- W e =Friction-reading= 


. . .ft.-lbs. 



192. Emerson's Power-scale. — One of the most complete 
transmission-dynamometers is shown in Fig. 135, with attached 
numbers showing the dimensions of the various sizes manu- 
factured. In this instrument the wheel C is keyed or fastened 
to the shaft ; the wheel B is connected with the wheel C near 
its outer circumference by projecting studs; the amount of 
pressure on these studs is conveyed by bent levers to a collar* 
which in turn is connected with weighing-levers. Small weights 
are read off from the scale D, and larger ones by the weights 
in the scale-pan N. A dash-pot is used to prevent sudden 
fluctuations of the weighing-lever. 

193. Form of Report. — The following forms for report 
and log of tests on Webber Dynamometer and Emerson's 
Power-scale are used by the Massachusetts Institute of Tech- 
nology. 

REPORT. 
Test on •••• , 



No. 



Date. 



No. of test.... 

Ft.-lbs. per .seconds 



WEBBER DYNAMOMETER. 
I 



!.....:. I 



EMERSON POWER-SCALE. 



No. of test 

Duration of test 

Revolutions per minute. 
Load 



26o 



EXPERIMENTAL ENGINEERING. 



[§ x 93. 




Emerson's Power-scales. 



§ I94-] 



MEASUREMENT OF POWER. 



26l 



BRAKE. 





I 

1 


2 


<2 






















T-l . . 








T 2 
























Coefficient of friction 









No. of test 

H. P. by dynamometer. 
H. P. by power-scale.. 
H. P. by brake... 



2-3 



Signed.. . 
LOG. 



Test on 



No. 



Date. 





Webber Dynamomete 


r. Emerson Power-scale. 


Brake. 






u5 






u 






















c 
























O 


c 




c 


<u 








3 






hi) 
c 

O 

O 

d 


a 


> 




4- 


V 

a 


3 


CJ 


c 
•3 

u 


a 

a 
.2 3 

3.2 


T3 




a 


c 

3 
O 

U 



tn 
bO 

a 
•3 

Pi 


3 

i 

1-. 

4) 

a 

CO 

3 
_o 

3 
O 
> 
V 

Pi 






< 






TestN 


umber 1 





—. 


Tes 




mber 










I 


2 


3 




1-3 


2-3 


H. P. by dynamometer 








H. P. by power-scale 














H. P. by brake 




]••• 













Constants and Remarks. 



194. The Van V/inkle Power-meter. — The Van Winkle 
Power-meter is shown in Fig. 136, complete, and with its parts 



262 



EX PERI MEN TA L ENGINEERING. 



[§ 194. 



separated, in Fig. 137. It consists of a sleeve with attached 
plate, B, that can be fastened rigidly to the shaft; and a 
plate ; A, which is revolved by the force communicated through 




Fig. 136.— Tan Winkle Power-meter. 



the springs ss. The angular position of the plated with refer- 
ence to B will vary with the force transmitted. This angular 
motion is utilized to operate levers, and move a loose sleeve 




I<IG. I37. 



-Parts of the Van Winkle Power-meter. 



longitudinally on the shaft. The amount of motion of the 
sleeve, which is proportional to the force transmitted, is indi- 
cated by a hand moving over a graduated dial. The dial is 
graduated to show horse-power per 100 revolutions. 



§196-] 



MEASUREMENT OF POWER. 



263 



195. Belt-dynamometers. — Belts ha-/e been used in some 
instances instead of gearing in transmission-dynamometers, 
but because of the great loss of power due to stiffness of the 
belts, and to the uncertainty caused 
by slipping, they have not been 
extensively used. The following 
form, from Church's " Mechanics 
of Materials," is probably as suc- 
cessful as any that has been de- 
vised. It consists of a vertical 
plate, carrying four pulleys and a 
scale-pan, as shown in Fig. 138. 
The scale-beam is balanced, the 
belt then adjusted, and power turned on ; a sufficient weight, 
G, is placed in the scale-pan to balance the plate again. Let 
b be the arm of the scale-pan, and a that of the forces P and 
P f . Then, for equilibrium, 




Fig. 138.— A Belt-dynamometer. 



Gb = Pa-P'a, (1) 

since .Pand P f on the right have no leverage about C 9 as the 
line of the belts produced intersects C. From (1) 



a 



(2) 



The work transmitted in foot-pounds per minute is equal 
to (P — P')v, in which v is the velocity of the belt in feet per 
minute to be obtained by counting. Another form employs 
two quarter-twist belts to revolve a shaft at right angles to the 
main shaft. (See Vol. XII., Transactions Am. Soc. Mechan- 
ical Engineers.) 

196. Method of Testing* Belts.* — The object of this test 
is to determine the coefficient of friction, and the power trans- 
mitted by various kinds of belting running under different 
conditions. 



264 EXPERIMENTAL ENGINEERING. [§ 197- 

The required formulae are given in Article 128, page 199, 
as follows : T x , maximum tension ; T 2 , minimum tension ; F, 
the force of friction ; c, the percentage of arc of contact to 
whole circumference ; 0, the arc of contact in circular measure 
We have 

T — T =F- 
T 

* 9 

Common log —: = 0.434/0 = 2.7288/*. 
From which 

or 

/= Napierian log (-^)^. 

Belt-testing machines must be arranged so that measures 
of T lt T 2 , 0, and c can be made. To determine loss due to 
resistance, it is necessary to supply the power by a transmis- 
sion-dynamometer, and absorb that delivered by a brake. 

197. The Sibley College Belt-testing Machine.— The 
belt-testing machine illustrated in Fig. 139 is used in the 
Mechanical Laboratory of Sibley College. It was designed by 
Wilfred Lewis of Philadelphia, and used in the tests described 
in Vol. VII. of Transactions of American Society of Mechanical 
Engineers. 

The belt to be tested is placed on the pulleys E, F; power is 
transmitted through the pulleys Pto the Lewis transmitting- 



* The student is referred to papers in Transactions of American Society of 
Mechanical Engineers, Vol. VII., by Wilfred Lewis and Prof. G. Lanza; also 
to paper in Vol. XII., by Prof. G. Alden ; and to the Holman tests in the Jout 
nal of the Franklin Institute, 1885. 



f W-] 



MEASUREMENT OF POWER. 



265 




266 EXPERIMENTAL ENGINEERING. [§ I9& 

dynamometer (see Article 188, page 252), and thence through 
the shaft Hto the pulley ii. The power transmitted is absorbed 
by a Prony brake on the shaft M. The slip of the belt is 
measured by transmitting the motion of the pulley E by gearing 
to the shaft /, and thence to a disk S, whose edge is graduated. 
The pulley F is connected to the gear-wheel L, shown in a 
larger scale in centre of Fig. 96. The wheel L is so proportioned 
that if there is no slip it will revolve at the same rate as the 
disk S; if there is slip it will fall behind 5. The amount that 
it falls behind is read by the scale V> which may be clamped 
to the hub of L by the screw T. As this device moves only 
one one-hundredth as fast as the main shafts, the amount of 5 
slip can be easily read. The pulley F and the brake M are 
mounted on a carriage, which can be drawn back by the screw 
N. The pulley E is mounted in a frame, supported on knife- 
edges below, R. The shaft H is fitted with a universal joint, 
to eliminate the effect of transverse strains on the dynamom- 
eter. 

Weighing-scales are placed at Ay £, and C, respectively, 
that at A is termed the dynamometer-scales ; that at B, the brake- 
scales that at C, the tension-scales. The reading on the tension- 
scales C, multiplied by the horizontal arm K, divided by the 
height d of the pulley E upon the knife-edge, gives the total 
tension on the belts T x -f- T 2 . The reading on brake-scales 
B, divided by the arm b of the brake, and multiplied by the 
radius D of the pulley F, gives the difference of tensions 
T 1 —T 2 . The brake-scale reading, multiplied by the brake-arm 
b y and by 2nn, n being the number of revolutions, gives tru 
delivered work in foot-pounds. The dynamometer scale-read- 
ing A y multiplied by the equivalent dynamometer-arm a and 
by 27T/Z, gives the work received in foot-pounds. The dyna- 
mometer-arm a is to be found as described in Article 1881 
page 253. 

198. Directions for Belt-test 

I. Before starting: 

(a) Get speed-indicator and log-blanks. 

(b) Oil all bearings and loose pulley under main belt. 



£ iq8.] measurement of power. 267 

(c) Balance scales A and C, and note their "zero- 
readings." 

2. With test-belt off : 

(d) Take friction-reading on scales A for driving-shaft, 
counting its revolutions. 

{e) Weigh brake-arm (see note below) to get zero- 
reading of scale B and then remove brake from brake-pulley. 

3. With brake off : 

(/) Put on test-belt (while loose), first moving brake- 
shaft frame by unscrewing hand-wheel next the floor. Tighten 
belt to read while at rest 75 lbs. net, on scales C. 

(g) Take friction-reading again on scales A. Count 
revolutions of driving-shaft and read " per cent of slip," from 
which the speed of brake-shaft can be calculated. 

4. Run I. 

(Ji) For tension of belt : Set scales C to read 50 lbs. net 
with belt at rest, by screwing up hand-wheel next the floor r 
which should not be changed during the run. Take reading 
of scales C for each load added on brake-scales B. 

(t) For power given out by belt : Set scales B to read 5 
lbs. " net " or effective " load," and balance by tightening 
brake while running. Feed a light stream of water into rim 
of brake-pulley. Count its revolution*. 

(k) For power put into .belt : Read scales A and take 
speed of driving-shaft. 

(/) For slip of belt : Read graduated " slip-disk,'* which 
has 100 equal divisions. When vernier is set, it turns with the 
disk, and shows one per cent of slip when falling back one 
division during one turn of the slip-disk. 

(m) Thus continue to increase brake-load by $ lbs. of 
increments on scales B. Each time keep it carefully balanced, 
and take simultaneous readings on scales A, scales B, scales C 9 
slip-disk, and revolution-counter. 

5. Runs II., III., and IV. 

(n) For run II., set tension-scales to read 75 lbs. net 
with belt at rest, and proceed as in run I. Increase this initial 
tension-reading by 25 lbs. each, for runs III. and IV. 



268 



EXPERIMENTAL ENGINEERING. 



L§ '99- 



6. Measurement of machine-constants : 

(p) Get length in feet of (i) brake-arm, (2) dynamom- 
eter-arm, (3) arms of bell-crank acting on tension-scales, and 
(4) circumferences of test-belt pulleys, — latter with steel tape. 
Calculate diameters. 

(p) If the pulleys differ in diameter, the reading on 
slip-disk, obtained while running " light " (see (g), above), will 
be the " zero" of all the slip-readings. 

N.B. Shut off water at brake-pulley when it stops. 

Note. — To weigh brake-arm : Loosen brake and oil face of 
pulley. Balance arm on scales while turning pulley first back- 
ward and again forward. The mean of the two readings will 
be the weight required. 

199. Form of Log and Reports as used in Sibley Col- 
lege. 

Test of Belting by 189. . 

Description of Belt, Material Made by 

Length feet. Width inches. Thickness inches. 

Condition : = 





6 

£ 


g-g. 

O u 
*3 c 

B> 

£Q 
Pi 

n 


c 

i 

d 
53 


•j 

$ 

a j 

c 

u 


Scale-readings, 
lbs. 


i 

+ 


+ 

3 


*3 <u 

bt 

c.H 
> 

H 


h 
P 

c u 
.2 > 

"Jo'C 

gQ 
H 




V 

H 

Sh , 
O CO 

•Si 

Pi. 


<u O 

u 


v 

S 0. 

S £ 

Q 




1 

s 

3 
5 


• 

a 


u 

Q 


2 

OQ 


d 

"3 
g 


0, 

B 

2 


I 
2 

3 
4 
5 
6 

7 
8 

9 
10 

11 

12 
13 

14 
15 
16 

17 

18 

19 
20 

Avg 


j 


c 


A 


B 


C 


T x -T % 


Ti+T 9 


T x 


^ 8 


T x +T* 


/ 




■ 



§ 1990 



MEASUREMENT OF POWER. 
CONSTANTS OF MACHINE. 



269 






Symbol. 




Results. 


a 


Arm of transmission-dynamometer ft. 




k 


Hor arm on tension-scales * ' 




d 






O 


Diameter driving pulley in. 




Dx 


Diameter driven pulley " 










Face driven pulley , " 

Area of bearings, driving wheel sq. in." 






'* " " driven wheel " " 






Weight on bearings, driving wheel lbs. 






" " " driven wheel " 






Kind of pulley used 














FORM OF REPORT. 

Results of Test of Belting. 

Made by ... .r 190. . 



Average of Results. 


Test No. 
I. 


Test No. 
II. 


Test No. 
III. 


Test No. 
IV. 


Duration of trial 










Revolutions driving shaft 










Revolutions driven shaft 










Belt-speed, feet per minute 










Dynamometer-scales, lbs 










Brake-scales, lbs 










Tension-scales, lbs 










Circumference driving pulley. .......... 










Circumference driven pulley 










Dynamometer horse-power. . . . .. 










Brake, horse-power 










Difference 










Slip of belt, per cent ...<,.,... , 










Slip of belt, feet per minute 










Horse-power per inch in width 










Maximum tension, 7\ 










Minimum tension, 7a 










7*i — 7i 0... 






• V 




T x 4- T« 










Arc of contact, degrees 










Coefficient of friction, per cent 










Loss due to stiffness 










Loss due to journal-friction 





















CHAPTER VIII. 

MEASUREMENT OF LIQUIDS AND GASES. 

200. Theory of the Flow of Water. — General Formula of 
Discharge. — The theory of the flow of water is fully investigated 
in Weisbach's Mechanics, Vol. I.; in Church's Mechanics of 
Engineering; and in the article " Hydromechanics," Encyclo- 
paedia Britannica. A very concise statement of the principles 
involved and formulae required are given here, preceding the 
actual methods of measurement of the flow, but students are ad- 
vised to consult the foregoing works. In the flow of water the 
particles are urged onward by gravity, or an equivalent force, 
and move with the same velocity as bodies falling through a 
height equal to the head of water exerting the pressure. If 
this head be represented by k, and the corresponding velocity 
in feet per second by v y we have, neglecting friction losses, 

v— V2gk (i) 

If we denote the area in square feet of the discharge ori- 
fice by F, the quantity discharged in cubic feet per second by 
Q, then, neglecting contraction. 

Q = vF=FV2gh (2) 

It is found, however, in the actual discharge of water, that, 
except in rare cases, 1. The actual velocity of discharge is less 
:nan the theoretical ; 2. The area of the stream discharged is 
less than the area of the orifice through which it passes. These 
losses are corrected by introducing coefficients. The coefficient 

270 



§ 200.] MEASUREMENT OF LIQUIDS AND GASES. 2/1 

of velocity is the ratio of the actual to the theoretical velocity, 
and is represented by c v . The coefficient of contraction is the ratio 
of the least area of cross-section of the discharged stream to 
the area of orifice of discharge, and is denoted by c c . The 
coefficient of efflux or discharge is the product of these two 
quantities, and is represented by c. 

If v a denotes the actual velocity of discharge, we shall have 

v a = c v V~2gh. . (3) 

The coefficient c v is to be determined by experiment ; it is 
nearly constant for different heads with well-formed simple 
orifices. It often has the value 0.97. The difference between 
the velocity of discharge and that due to the head may be 
expressed in terms of the equivalent loss of head. Thus the 
total head producing outflow consists of a part, h a , producing 
the actual velocity v a \ and a second part, h r , expended in 
overcoming velocity and friction. Denote the ratio of these 
parts by c T . Then 



K = cjk* (4) 

We also have 

k = h r + k a = klc r +i). ..... (5) 

Hence 

Since k a is the head-producing velocity, 

Va—^^a=\/2g——. . e . . (7) 



2 7 2 EXPERIMENTAL ENGINEERING. [§ 201. 

By equating (7) and (3) we obtain the relation of c r to c 9 
as follows: 

^=t?- 1 • • (8) 

Tke actual discharge 

Q a = cQ = cvF=cFl/?g%. (9) 

Since c s=s £„£ c , 

Q a = cfF\f^h = cfJ 2 g7 ^. . (10) 
From equation (9), 

'-&+<& 

201. Formulae for Flow of Water over Weirs.* — A weir 
is primarily a dam or obstruction over which the water is made 
to pass ; but the term is often applied to a notch opening to 
the air on one side, through which the water flows. In cases 
where the opening is entirely below the surface, it is spoken of 
as a submerged weir. The head of water producing the flow 
is the distance to the surface of still water from the centre of 
pressure of the issuing stream. The depth of the weir is meas- 
ured from the surface of still water to the bottom or sill of the 
notch. 

Rectangular Notch. — Denote the coefficient of efflux bye, 
the depth of the weir in feet by h, the area in sq. feet enclosed 
by the wetted perimeter by F 9 and the number of cubic feet 
per second by Q. We have, as a formula applicable to open 
rectangular notches, 

Q = %FcV^h (11) 

* See Church's Mechanics, page 684; Rankine's Steam-engine, p. 90; Encyc. 
Britannica, Vol. XII. p. 470; Bulletin on Irrigation and Use of Weirs, by Prof. 
L. G. Carpenter, Fort Collins, Colorado. 



§ 201.] MEASUREMENT OF LIQUIDS AND GASES. 2 J 3 

With most areas c increases slightly with the length and 
diminishes with the head ; it probably depends on the ratio of 
wetted perimeter to area, although it is not quite constant for 
triangular notches, in which this ratio is a constant one. Very 
complete and extensive experiments were conducted by J. B e 
Francis at Lowell, Mass., and from these experiments he de- 
duced the value of the coefficient of contraction to equal one 
tenth the head, and consequently for rectangular weirs 



Q = \c{b — o.mk)h \2gh y .... (12) 

in which n = number of contractions. Applying this correc 
tion to an ordinary rectangular notch with two contractions. 
we have the well-known Francis formula for rectangular weirs, 

Q = \c{b — o.2h)h sfTgh = 5.35^ — 0.2 k)$ . . (13) 

For heads ranging from three inches to two feet it has been 
found by experiment that 

c = 0.62 and Q — ig{b — o.2h)h*. 

Triangular Notch. — For the triangular notch in which apex 
is down, b the base at water-level, h the depth, 

Q = (4 -5- i$)cbk V2gh = 4.28MK ... (14) 

If the angle is 6o°, 

b = 2h tan 30 = 1.1547^ and Q = 2^ckK 

If the angle is 90 , 

b = 2h and Q = -^ch* ^2gh. 

Trapezoidal Notch. — To avoid the corrections for contrac- 
tions, Cippoletti of Milan in 1886 proposed to use a trape* 



2;4 



EXPERIMENTAL ENGINEERING. 



[§202 



zoidal notch of such dimensions that the area of the stream 
flowing through the triangular portion should be just sufficient 
to correct for the contraction of the stream in a rectangular 
weir. The proportions of such a weir, in terms of the length 
at bottom of the notch, is as follows : height equal to six tenths 
the bottom length, width of top equal to the bottom plus 
one fourth the height added to either side; the tangent of the 
angle of inclination of the sides equal to O.25. It is asserted 
that such a weir will give the discharge with an error less than 
one half of one per cent. The formula for the use of such a 
notch would be simply 



Q = \cbh V2gk = 3.33M*. 



(15) 



Submerged orifices, rectangular or circular, are sometimes 
used for the measurement of water. The required formulae 
are given in the table following. 

From table in Weisbach's Mechanics, c = on the average 
0.6. For small areas it diminishes with increase of head from 
0.7 to 0.6, and for large areas it increases with increase of head 
from 0.57 to 0.60. 

These formulae are conveniently tabulated as follows : 

202. Table of Formulae for Flow over Weirs. 







O . 


°2 

5 


% c v * 




Form of Notch. 


u 

+3 ° 


C V 
- C 

si 




a. g-g 

£3.a 


Formula for discharge in cubic 
feet per second. 






~ a 


•a ° v 










aoj. 

V *j 


£§« 


> O O 






Q 


Q 


£G~ 


< 




Rectangular; 












Usual form . . . 


h 


O 


b 


.63 to .58 


Icbh \/^fh 


Francis 


h 


O 


b 


.622 


%ch ^2gh{b — 0.\nh) 


Submerged.. . 


h 


ti 


b 




%cb\/2g(?$-h'*) 


r 


h 


h' 


b 


.62 


cb{h-h')\/g(h+h'} 


Triangular: \ 


h 


O 


b' 


.617 


•hcb'h \f2gh__ 


I 


h 


O 


2.h tan a 


.617 


■fecbh? tan a \/2gh 


Ang. at b. 6o° 


h 


O 


i.i547^ 


.617 


2.\-]c$ 


Ang. at b. 90 


h 


O 


ih 


.617 


ftbh* V^gh 


Trapezoidal: 












Cippoletti's. . . 


h 


O 


* + \h 


0.629 


%cbh ^2gh 



§ 204- j MEASUREMENT OF LIQUIDS AND GASES. 27$ 

When still water cannot be found above the weir, and we 
have a velocity of approach that can be measured and is equal 
%>' — V2gh\ we can compute h\ Then 

Q=$.l$cb\_{k + k'f-k'*l* .... (16) 

In above formula Q = discharge in cubic feet per second, 
b the length of sill at bottom of notch. 

203. Efflux of Water through Nozzles, or Conical Con- 
verging Orifices. — In this case, if we denote least area in 
square feet by F, in which c" is the coefficient of contraction, 
c f that of velocity, and c that of discharge, 

Qz=c'c' , FV~2~gk = cFV2gh (17) 

In this case the head is to be measured by a pressure-gauge 
attached close to the nozzle. 

The value of c is a maximum when the sides of the nozzle 
make an angle of 13 24/, attaining a value of 0.946. When the 
angle of the nozzle is 3 io', c = 0.895, and when 49 , c = 0.895. 
(See Church's Mechanics, page 692 ; " Hydromechanics," 
Encyc. Brit., page 475.) 

204. Efflux of Water through Venturi Tubes or Bell- 
mouthed Orifices. — A conically divergent orifice, with 
rounded entrance to conform to the shape of the contracted 
vein, is now termed, from the first experimenter, Venturis tube. 
The dimensions of such a tube, as given in Encyc. Britannica, 
Vol. XII., page 463, are as follows, in terms of the small 
diameter (d). Large diameter (D) at opening equals 1.25*/; 
length equals .625^, or .$D. The sides are in section a circular 
arc, struck with a radius of 1.625^, from a centre in the line of 
(a) produced. 

* Rankine's Steam-engine. Hamilton Smith writes formula 
Q = 5.35^0*+ iKA 



276 EXPERIMENTAL ENGINEERING. [§ 205. 

The formula of discharge is 

Q = c f FV^~k, ....... (18) 

in which F is the least area, h the head to be measured by a 
pressure-gauge attached to the pipe before the area of cross- 
section is reduced, c' the coefficient of velocity. The coeffi- 
cient of contraction in this case is equal to one. Weisbach 
gives the value of c' as .959, .975, and .994 for heads respec* 
tively 2 feet, 40 feet, and 160 to 1000 feet. 

Prof. Church, in his Mechanics, page 694, describes an ex- 
periment on a conically divergent tube 3 inches long, .8 inch 
diameter at least section. 

Coefficient of discharge with heads from 2 to 4 feet varied 
from .901 to .914. 

205. Flow of Water under Pressure. — The pressure ex- 
erted by flowing water in pipes is very different from that due 
to still water under the same head. The pressure follows more 
or less closely the law enunciated in the theorem of Bernouilli, 
which may be stated in a general form as follows : " The exter- 
nal and internal work do7ie on a mass is equal to the change of 
kinetic energy produced ;" that is, the total energy of a flowing 
stream remains constant except for losses due to friction. 

In the flow of water through a pipe with varying cross- 
section the velocity of flow will be very nearly inversely as the 
area of cross-section. Since the energy or product of pressure 
and velocity is nearly constant by Bernoulli's theorem, as the 
velocity increases the pressure must diminish, and we shall 
find least pressure at the points where the cross-sections are 
least. From some experiments made by the author, the same 
law of varying pressure with varying cross-section applies in a 
less degree to the flow of steam through a pipe.* The formula 
expressing Bernouilli's theorem, neglecting friction, is 

& . P . 

— A \- z = constant; 

— 

*See "Hydromechanics," Encyc. Britannica, page 468. 



§ 2o6.] MEASUREMENT OF LIQUIDS AND GASES. 2JJ 

in which v 1 -f- 2g is the velocity-head, / is the pressure per 
square foot, y the weight per cubic foot ; so that / -f- y is the 
pressure-head, and z the potential head, or vertical distance 
from any horizontal reference line. 

206. Flow of Water in Circular Pipes.* — In this case 
there is a loss of head, h', due to friction. Denote the sine of 
the angle of inclination by t, diameter by d, length by L, loss 
of head by k/, all in feet coefficient of loss of head by £ 



,,-^_ 



From experiments of Darcy, 



(19) 



C = 0.005 ( 1 + — %] for clean pipes; 

C = 0.0 1 ( 1 -| %) for incrusted pipes ; 

C = o.a\i + Y^j in general ; 



-y/i 



%#i (20) 



Q = jfv. (21) 



Loss of Head at Elbows. — In this case the loss is principally 
due to contraction. Weisbach gives the following formula? : 



*' = c£ • • (22) 



See " Hydromechanics, " Encyc. Britannica. 



2J 8 EXPERIMENTAL ENGINEERING. 

If equal the exterior angle, 



[§ 206. 



C. = 0.9457 sin 3 — + 2.047 sin 4 -|. . . . (23) 



From this are deduced the following values 



20° 
O.O46 


40° 
O.I39 


6o° 
0.364 


8o° 
0.740 


90° 
0.984 


IOO° 

1.26 


110° 

1.556 


120° 

I. 861 



130° 
2.158 



For pipes neatly bent the value of Q e is much less. 

By equating k/ and hj in equations (19) and (22), a length 
of pipe can be found which will produce a loss of head equiva- 
lent to that produced by any given elbow. We shall have 
this additional length : 



Z = 



4C* 



(24) 



On substituting the values of C e as above, and £ as equal to 
0.006, this additional length will be found not to vary much 
trom 40 diameters for each 90 elbow, and 7 diameters for each 
45 elbow. 

Loss of Head on entering a Pipe. — This loss is very small 
when a special bell-mouthed entrance is used, but is great in 
other cases. The loss of head in entering a straight tube is 
expressed by the formula 



' = C 



zg 



(25) 



§ 20%] MEASUREMENT OF LIQUIDS AND GASES. 



279 



Weisbach found Q c = 0.505. By making h p ' of equation (19) 
equal to n a \ and reducing, we find the additional length, L, of 
straight pip^ producing the same loss of head. 



L = 



4C* 



Assuming C lias an average value of 0.006, and Q e as above, 

L = 2od. 



Loss of Head by abrupt Contraction of Pipe.- 
Weisbach found 



-In this case 



/ = 0.316^, 



which would correspond to an additional length of pipe equal 
to about 13 diameters. When the mouth of the contracted 
pipe is reduced by an aperture smaller than the pipe, Weis- 
bach found the following values of C c . In the table, F 1 is area 
of orifice, F 2 that of pipe into which the flow takes place. 



Ei + F 2 

C C • • 



O.I 
O.OI6 

23I.7 

gsod 



0.2 
0.614 

50.99 

2I2d 



0.3 
0.612 

I9.78 

S2d 



O.4 

0.6IO 

9.6l2 

40</ 



0.5 

O.607 
5.256 

22d 



O.6 

O.605 

3-077 
13d 



0.8 
0.601 
1. 169 

$d 



1.0 

0.59 6 
0.480 

2d 



Globe valves produce about one half more resistance than 
a right-angled elbow, or an amount equal to an additional 
length of about 60 diameters. 

207. Loss of Head in flowing through a Perforated 
Diaphragm in a Tube of Uniform Section. — Let F t be the 
area of the orifice, F that of the pipe in square feet, C the co- 
efficient of discharge, c the coefficient of contraction. 



280 EXPERIMENTAL ENGINEERING. [§ 208. 

The loss of head in feet 

*"fe"V** c v ; (26) 

Weisbach gives the following values as the results of ex« 
periments : 



F 


O.I 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


C e 
5 


0.624 

225.9 


0.632 

47.77 


0.643 
30.83 


0.659 
7.801 


0.681 
1.753 


0.712 

1.796 


0.755 
0.797 


0.813 

0.290 


0.892 
0.060 


1.0 

0.0 



208. Volume flowing through a Perforated Diaphragm. 

— Let H a represent the head in feet on side of greatest press- 
ure, and H b that on the opposite side. 
The loss of head 

h c = H a — H b . 
From equation (26), by transposing and substituting, 

2gh t 



v = 



The quantity discharged in cubic feet per second, 



(27) 



Q=,F,v = F 1 y/^(ff.-ff i ). 



From this 






(28) 



(28«) 



£ 2IO.J MEASUREMENT OF LIQUIDS AND GASES. 28 1 

209. Measurements of the Flow of Water. — General 
Methods. — The measurement of the flow of water is of import- 
ance in connection with efficiency-tests of pumps, water-meters, 
and steam-engines, as well as in determining the amount of water 
that can be obtained from a given stream. 

The methods used for measurement of the flow usually con- 
sist in making the water pass through open notches over weirs, 
through standard orifices or nozzles, or through meters. 

The coefficients that have been given are in every case to be 
considered approximations only, and should be tested by actual 
measurement under the conditions of use. 

The head of water is the distance from the centre of press- 
ure to the surface of still water under atmospheric pressure. In 
case the water is under pressure and at rest, this head can be 
measured by a calibrated pressure-gauge. The gauge is usually 
graduated to show pressure in pounds per square inch, each 
pound being equivalent to a head of 2.307 feet of water at a 
temperature of yo° Fahr., or to 2.037 inches of mercury. 

In case the water-pressure is read in inches of mercury, one 
inch of mercury corresponds to a head equal to 1.113 feet. 

A convenient table, showing relation of pounds of pressure- 
head in feet of water or inches of mercury, will be found in 
Article 260. 

210. Flow of Water over Weirs. — Methods of measuring 
the Head. — The head is measured most accurately by the use of 
the hook-gauge, used first by Mr. U. Boyden of Boston in 
1840. Many of the English engineers still depend on the use 
of floats. The head in all cases is to be measured at a distance 
sufficiently back from the weir to insure a surface which is un- 
affected by the flow. The channel above the weir must be of 
sufficient depth and width to secure comparatively still water. 
The addition of baffle-plates, some near the surface and some 
near the bottom, under or over which the water must flow, or 
the introduction of screens of wire-netting, serves to check the 
current to great extent. Such an arrangement is sometimes 
called a tumbling-bay. 

The object of the baffle-plates is to secure still water for the 



282 



EXPERIMENTAL ENGINEERING. 



[§2II. 



accurate measurement of height of the surface above the sill of 
the weir. The same object can be accomplished by connecting 
a box or vessel to the water above the weir by a small pipe 
entering near the bottom of the vessel ; the water 
will stand in this vessel at the same height as that 
above the weir, and will be disturbed but little by 
waves or eddies in the main channel. The height 
of water is then obtained from that in the vessel. 
Prof. I. P. Church has the connecting-pipe pass over 
the top of the vessel and arranged so as to act as a 
siphon. 

The Hook-gauge. — This consists of a sharp- 
pointed hook attached to a vernier scale, as shown 
inFig. 140, in such a manner that the amount it is 
raised or lowered can be accurately measured. To 
use it, the hook is submerged, then slowly raised to 
break the surface. The correct height is the read- 
ing the instant the hook pierces the surface. To 
obtain the head of water flowing over the weir, set 
the point of the hook at the same level as the sill 
of the weir. The reading taken in this position 
will correspond to the zero-head, and is to be sub- 
tracted from all other readings to give the head of 
the water flowing over the weir. 

In some forms of the hook-gauge the zero of 
the main scale can be adjusted to correspond to 
Hook-gauge. ^q ze ro-head, or level of the sill of the weir. 
Floats. — Floats are sometimes used : they are made of hol- 
low metallic vessels, or painted blocks of wood or cork, and 
carry a vertical stem ; on the stem is an index-hand or pointer 
that moves over a graduated scale. 

211. Conditions affecting the Accuracy of Weirs.— 
I. The weir must be preceded by a straight channel of con- 
stant cross-section, with its axis passing through the middle of 
the weir and perpendicular to it, of sufficient length to secure 
uniform velocity without internal agitation or eddies. 

2. The opening itself must have a sharp edge on the up- 



§ 2 1 3. J MEASUREMENT OF LIQUIDS AND GASES. 283 

stream face, and the walls cut away so that the thickness shall 
not exceed one tenth the depth of the overflow. 

3. The distance of the sill or bottom of the weir from the 
bottom of the canal shall be at least three times the depth on 
the weir, and the ends of the sill must be at least twice the 
depth on the weir from the sides of the canal. 

4. The length of the weir perpendicular to the current shall 
be three or four times the depth of the water. 

5. The velocity of approach must be small ; for small weirs 
it should be less than 6 inches per second. This requires the 
channel of approach to be much longer than the weir opening. 

4. The layer of falling water should be perfectly free from 
the walls below the weir, in order that air may freely circulate 
underneath. 

. 5. The depth of the water should be measured with accuracy, 
at a point back from the weir unaffected by the suction of the 
flow and by the action of waves or winds. 

6. The sill should be horizontal, the plane of the notch 
vertical. 

212. Effect of Disturbing Causes and Error in Weir 
Measurements. — I. Incorrect measurement of head. This 
may increase or decrease the computed flow, as the error is a 
positive or negative quantity. 

2. Obliquity of weir ; the effect of this or of eddies is to 
retard the flow. 

3. Velocity of approach too great, sides and bottom too 
near the crest, contraction incomplete, crest not perfectly 
sharp, or water clinging to the outside of the weir, tend in each 
case to increase the discharge. 

The causes tending to increase the discharge evidently out- 
number those decreasing it, and are, all things being taken into 
account, more difficult to overcome. 

213. Water-meters. — The water-meter is an instrument 
for measuring the amount of water flowing through a pipe. 
Knight makes seven distinct classes of water-meters, as follows:* 

* Knight's Mechanical Dictionary, Vol. III. 



284 EXPERIMENTAL ENGINEERING. [§ 2 1 4. 

1. Those in which the water rotates a horizontal case, or a 
horizontal wheel in a fixed case, delivering a definite amount 
at each rotation. 

2. A piston or wheel made to rotate by the pressure of the 
water, the meter in this case being the converse of the rotary 
engine or pump. 

3. A screw made to rotate by the motion of the water. 

4. A reciprocating piston in a cylinder of known capacity 
driven backward and forward by the pressure of the water. 

5. The pulsating diaphragm, in a vessel of known capacity, 
which is moved alternately as the side chambers are filled and 
emptied. 

6. The bucket and balance-beam, in which the buckets of 
known capacity on the ends of the beam, are alternately pre- 
sented to catch the water and are depressed and emptied as they 
become filled. 

7. The meter-wheel, in which chambers of known capacity 
are alternately filled and discharged as the wheel rotates. 

Besides these seven classes, it is evident that any machine 
may be used in which the motion is proportional to the velocity 
of flow of water. 

These classes can be united into two general classes: I. Posi- 
tive; II. Inferential. In class I. the water cannot pass without 
moving the mechanism, and meters of this kind are considered 
more delicate and accurate than those in class II. 

Each class of meter has a registering apparatus, which in 
general consists of a series of gear-wheels, so arranged as to 
move a hand continuously around a graduated dial, from which 
the volume can be read. 

214. Errors of Water-meters. — In addition to the constant 
errors of graduation, meters are liable to be clogged by dirt, to 
be affected by air in the water, and by change in the tempera- 
ture, head, or quantity of discharge of the water passing 
through. 

While the meter is no doubt of sufficient accuracy for com- 
mercial purposes, it should be used with caution in the measure- 
ment of water for tests or for purposes of scientific investiga* 



§ 21 $.] MEASUREMENT OF LIQUIDS AND GASES. 285 

tion. Before and after such tests a careful calibration of the 
meter should be made under the exact conditions of the test. 

The following directions explain the method of calibrating 
the weir notch and meter, arranged in series. In this experi- 
ment the water is to be weighed. Either instrument may be 
calibrated separately. In case the weir has been calibrated, the 
meter could be calibrated by direct comparison, without the 
use of weighing-scales. 

215. Directions for Calibrating the Weir Notch and 
Meter. — The object of this experiment is to determine the 
coefficient c of formula (9), Article 201, page 272, and the ac- 
curacy of previous determinations. 

Apparatus needed. — Hook-gauge, pair of scales, thermom- 
eter, spirit-level, pressure-gauge, weir, and meter. 

1. Accurately level the sill of the weir, and see that the 
notch is in a truly vertical plane. 

2. Take the zero-reading of the hook-gauge, by setting the 
point of the hook with a spirit-level, at the same height as the 
sill of the notch. In case the form of the notch is such as to 
prevent the use of the spirit-level, grease the edge of the notch 
and set the hook by the water-level ; being sure that the water 
surface does not, through capillary action, rise above the 
lower edge of the notch. 

3. Start the water flowing, and after it has obtained a con- 
stant rate, take measurements of weights and of head. The 
commencement of the experiment to be determined by the 
rising of the poise on the scale-beam, which previously must be 
set at a given weight. Note the time, scale reading, thermom- 
eter-reading, reading of the hook-gauge at the beginning and 
once in five minutes during the run. As the experiment ap- 
proaches the end set the poise of the scale-beam in advance of 
the weight, terminate the run when the beam rises, accurately 
noting the time, weight, thermometer-reading, and reading of 
the hook-gauge. Make direct measurements of the coefficient 
of contraction. Calculate coefficient of discharge, 

4. If the water to the weir first passes through a meter, take 
corresponding readings of the meter-dial, Note the pressure 






286 



EXPERIMENTAL ENGINEERING. 



[§ 216, 



and temperature at the meter. Calculate the number of cubic 
feet. 

5. Draw on cross-section paper a curve of discharge, in 
which cubic feet per second are taken as abscissae and the cor- 
responding heads as ordinates. Also draw in dotted lines on 
the same sheet a curve of coefficients, of dschargein which co- 
efficients are taken as abscissae, and corresponding heads as 
ordinates. Also, draw a curve showing error of meter for each 
head, 

216. Form of Report. — The following form has been 
used by the author for calibration of the weir notch and meter : 

CALIBRATION OF WEIR NOTCH AND METER. 

Made by 

at Date 



Number of Run. 


I. 


II. 


III. 


IV. 


V. 


Duration, minutes. 












Temperature discharge, dee;. F 












Readings of hook-gauge — Zero ft. 












" " Max ft. 












Min ft. 












Av ft. 




































•' " Total lbs. 












Cubic feet per second Q. 
























End ft. 












Area — Wetted orifice sq. ft. 

" Contracted section sq. ft. 

Coefficients — Contraction, c c 












" Discharge, ^ 
















































" End 





















































































Constants of Weir, Form ....... Length ft. Angle of sides. 

Remarks 

Meter, manf. by General class 

Remarks < Formulae: c = c c c v , c r - 



No.... 

1 

= I. 

Cv 



§ 2I8.J MEASUREMENT OF LIQUIDS AND GASES. 287 

217. Calibration of Nozzles and Venturi Tubes. — These 
are often more convenient to use than weir-notches, in the 
measurement of the efflux of water. Before using these they 
should be carefully calibrated by measurements of the head 
and discharge. The Venturi tube is sometimes inserted in a 
length of pipe ; in this case the pressure should be observed 
on either side of the tube, and the discharge measured. The 
special directions for calibrating when discharging into the air 
would be as follows : 

1. Arrange the nozzle or Venturi tube, so that the discharge 
can be caught in tanks and measured or weighed. 

2. Attach a pressure-gauge, which has been previously cali 
brated, to the pipe near the nozzle. Since the pressure is a 
function of the area of cross-section, the position of the gauge 
should be described and the area of the cross-section at that 
point measured. 

3. Make careful measurements of least and greatest inter- 
nal diameters of nozzles, of length of nozzle, and note condition 
of interior surface. Make sketch showing the form. 

4. Make five runs, as explained in directions for calibrating 
weir-notches, Article 215, page 285, obtaining weight of water 
by the same method. In case it is not convenient to weigh the 
water, discharge into tanks which have been carefully calibrated 
by weighing, arranged so that one is emptying while the other 
is filling. 

5. Observe during run, reading of pressure-gauge, temper- 
ature of discharge-water, weight of discharged water. Com- 
pute corresponding head producing flow, volume of discharged 
water, and the coefficient of discharge in the formula 

Q = cFV2gh. 

6. Draw a curve showing relation of discharge in cubic 
feet to head, as explained for weir-notches, page 285 ; also one 
showing relation of coefficient to head. 

218. Measurement of Efflux of Water through an Ori- 
fice in End of Tube of Uniform Section. — A cap can often 



2 88 EXPERIMENTAL ENGINEERING. [§219. 

be arranged over the end of a tube, and an orifice made In 
this cap with a sharp edge on the side toward the current* 
This will be found to give very uniform coefficients of dis- 
charge. The special method of calibrating this orifice would 
be as follows : 

1. Arrange the tube with a cap in which is an orifice, the 
area of which is one third that of the pipe. Ream the sides of 
the orifice so that a sharp edge will be presented to the out- 
flowing water. Attach a calibrated gauge at a distance of two 
diameters of the pipe back from the orifice. Arrange to weigh 
or measure the discharged water. Measure the orifice. 

2. Make runs as explained for other calibrations with five 
different heads, and note reading of pressure-gauge, temperature 
of discharged water, weight or volume of discharged water, and 
least diameter of stream discharged. The least diameter of the 
discharged stream can be measured by arranging two sharp* 
pointed set-screws in a frame, so that they can be screwed 
toward each other. These screws can be made to touch the 
outflowing stream, and the distance between their points meas- 
ured. 

3. Compute head producing the flow, coefficient of con- 
traction, which is ratio of area of stream to area of orifice,, 
coefficient of discharge, and loss of head. See equations (i) 
to (10), Article 200, page 272. 

4. Draw curves on cross-section paper showing the relations 
of these various quantities. 

5. Repeat the experiment with orifices of different sizes. 
219. Measurement of the Flow of Water in Pipes by 

use of a Perforated Diaphragm or of a Venturi Tube. — la 
this case the loss of head flowing through the orifice in the 
diaphragm or the Venturi tube must be measured ; then, know- 
ing the coefficient of efflux and area of cross-section, the vol- 
ume discharged can be computed by equation (28), Article 
208, page 280; also Art. 204, p. 275. 

Q = F l ^ 2 -*(H a -H l ).. . . . . (28) 



i, 220.] MEASUREMENT OF LIQUIDS AND GASES. 289 

The difference of head is measured accurately by inserting 
tubes at a distance of two diameters on each side of the orifice, 
connecting each of these tubes to a U-shaped glass tube partly 
filled with water, very much as shown 5n Fig. 145, page 294, 
except that the ends of the tubes A and B are in each case 
perpendicular to the pipe, and are on opposite sides of the 
diaphragm. The difference in the height of the water in the 
two branches of the U-shaped tube will be the loss of head 
(H a — H b ) caused by the orifice. It is essential that the tubes 
be connected into pipes having equal areas of cross-section, 
since the pressure, even in the same line of pipe, increases with 
the area (see Article 205). The coefficient Q should be deter- 
mined by calibration, following essentially the same method as 
that prescribed for nozzles and Venturi tubes in Article 217. 

220. Measurement of the Flow of Water in Streams.* — 
This is done by (1) Floating bodies ; (2) Tachometer ; (3) Pitot's 
tube ; (4) Hydrometric pendulum. 

Floating bodies, when used, should be small, and about the 
density of the water. A floating body with a volume about 
one tenth of a cubic foot is better than larger. They can be 
made of wood and weighted, or of hollow metal and partially 
filled with water. A coat of paint will serve to render them 
visible. To obtain the velocity for different depths, the sur- 
face velocity is first found, the float is then connected with a 
weighted ball that can be adjusted to float at any depth, and 
the joint velocity observed. 

Call the surface velocity v , the joint velocity v m ; then will 
the velocity of the submerged ball be 

v x = 2V m — v . 

A floating staff that remains vertical in still water is some- 
times used. 

In case floats are used, the velocity is obtained by noting 
the time of passing over a measured distance. The measured 
distance should be marked by sights, so that the line of begin- 

* See Weisbach's Mechanics, Vol. I. 



290 EXPERIMENTAL ENGINEERING. [§ 221. 

ning and ending can be accurately determined. The float 13 
put in above the initial point, and the instant of passing the 




Fig. 141.— The Tachometer. 

firs; auid last lines of the course is to be determined by a stop- 
watch. 

221. The Tachometer, or Woltman's Mill, consists of a 
small water-wheel connected to gearing so as to register the 



§ 221.] MEASUREMENT OF LIQUIDS AND GASES. 29 I 

number of revolutions. The wheel is anchored at the required 
depth in the stream, and at a given instant, the time of which 
is noted on a stop-watch, the gearing is set in motion by pull- 
ing on a lever ; at the instant of stopping the experiment, the 
gears are stopped by a trip. The machine is removed, and 
the number of revolutions multiplied by a constant factor gives 
the total space moved by the water ; this divided by the time 
gives the velocity. 

The shape of the vanes of the revolving wheel are varied 
by different makers, and the wheel is made to revolve either in 
a horizontal or a vertical plane. 

Fig. 141 shows a form used extensively, in which the gearing 
for registering the number of revolutions is operated by an 
electric current, and can be seen at any instant. 

The electric register shown in Fig. 142 can be located at 
any distance from the tachometer convenient to the observer. 

Calibration.— The constant factor, which multiplied into 
the dial-reading gives the velocity, is obtained by calibration. 
The calibration is performed by attaching the instrument to 
a float or a boat, and towing it past fixed marks at a known dis- 
tance from each other. The velocity is obtained as for floating 
bodies, and the constant is found by comparing this with the 
readings of the instrument. One method of calibrating the 




Fig. 143, 

instrument is as follows (see Fig. 143) : The instrument is 
attached to the bow of a boat, so as to remain in a vertical 
position ; the water being still, and little or no current. The 
boat is propelled by a cord, which may be wound up by a 
windlass; the motion must be in a right line, and over a known 



292 



EXPERIMEN TA L ENGINEERING. 



[§ 222. 



distance. Several trials are to be made, and the average results 
taken, and reduced by the method of Least Squares, as ex- 
plained in Chapter I. 

The tachometer is the most convenient, and if properly 
constructed the most accurate, method of measuring the ve- 
locity of running water. 

222. Pitot's Tube. — This is a bent glass tube, held in the 
water in such a manner that the lower part is horizontal and 
opposite the motion of the current. By the impulse of the 
current a column of the water will be forced into the tube and 

held above the level of the water in 
the stream ; this rise, DE (see Fig. 
144) is proportional to the impulse 
or to the velocity of the water that 
produces it. If the height DE above 
the surface of the water equal h and 
the velocity of the water equal v, 
we have 




Fig. 144.— Pitot's Tube. 



v = c Vgh, 

in which c equals the coefficient to be 
determined by experiment. 

To determine the coefficient c, 
the instrument is either to be held 
in moving water whose velocity is known, or else moved 
through the water at a constant velocity. From the known 
value of v and the observed value of h the coefficient c can be 
calculated. 

Weisbach found that with fine instruments, when the 
velocities were between 0.32 and 1.24 meters (1.04 and 4.068 
feet) per second, that 

v = 3.54.5 Vh meters per second, 

or, in English measures, 

v = 6.43 Vh feet per second. 



§ 222.] MEASUREMENT OF LIQUIDS AND GASES. 



293 



Pitofs tube, as ordinarily used, is shown in the diagram 
Fig. 145. It consists of two tubes, one, AB, bent as in Fig. 
144, the other, CD, vertical. The mouth-pieces of both tubes 
are slightly convergent, to prevent rapid fluctuation in the 




Fig. 145. — Sketch of Pitot's Tube. 

tubes. These tubes are so arranged that both can be closed at 
any instant by pulling on the cord ss leading to the cock R. 
Between the glass tubes dD and bB is a scale which can be read 
closely by means of the sliding verniers m and n. The tubes 
are connected at the top, and a rubber tube with a mouth-piece 
O is attached. 

In using the instrument it is fastened to a stake or post by 
the thumb-screws EF\ the bent tube is placed to oppose the 
current of water, the cocks K and R opened. The difference 
in height of the water in the tubes will be that due to the 
velocity of the current. The water in the column dD will not 
rise above the surface of the surrounding water, and the instru- 
ment may be inconvenient to read. In that case some of the 
air may be sucked out at the mouth-piece O, and the cock K 
closed ; this will have the effect to raise the water in both 



294 



EXPERIMENTAL ENGINEERING. 



L§ 223. 



columns without changing the difference of level, so that the 
readings can be taken in a more convenient position; or by clos- 
ing the cock K, by pulling on the strings ss, the instrument 
may be withdrawn, and the readings made at any convenient 
place. 

223. Pitot's Tube for High Pressures. — A modified 
form, as shown in Fig. 146, of Pitot's tube is useful for obtain- 
ing the velocity of liquids or gases flowing under pressure. 
The arrangement is readily understood from the drawing. 




Fig. 146. — Sketch of Pitot's Tube for High Pressures. 

The difference of pressure is shown by the difference in heights 
of the liquid in the branches of the U-shaped tube MM'; this 
difference is due entirely to the velocity, since both branches 
are under equal pressure. Thus, if the liquid stand at M on 
one side and at M' on the other, the velocity is that due to the 
height of a column of liquid equal to the distance that M is 
above M'. Call this distance h; then 

The coefficient c is to be determined by experiments made 
on a tube in which the velocity of flow is known. 



§ 225-] MEASUREMENT OF LIQUIDS AND GASES. 295 

224. Hydrometric Pendulum. — This instrument consists 
of a ball, two or three inches in diameter, attached to a string. 
The ball is suspended in the water and carried downward by 
the current; the angle of deviation with a vertical may be 
measured by a graduated arc supported so that the initial or 
zero-point is in a vertical line through the point of suspension. 
If the current is less than 4 feet per second an ivory ball can 
be used, but for greater velocities an iron ball will be required. 
The instrument cannot give accurate determinations, because 
of the fluctuations of the ball and consequent variations in the 
angle. The formulae for use are as follows : Let G equal the 
weight of the ball, D equal the weight of an equal volume of 
water ; then G — D is the resultant vertical force. Let F equal 
area of cross-section of the body, v the velocity of the current, 
c a coefficient to be determined by experiment ; then we have 
the horizontal force P = cFv 2 . Let angle of deviation be d ; 
then 

P cFv* 

tand = ___=___, 

from which 



V = \/ [ 



(G - I?) tan d 
cF 



The best results with this instrument will be only approxi- 
mations. 

225. Flow of Compressible Fluids through an Orifice.— 

General Case. — In this case, as heat is neither given nor taken 
up, the flow is adiabatic. The formulae are deduced by prin- 
ciples of thermodynamics, and their derivation can be studied 
in treatises devoted to those subjects.* 

Denote the velocity by v, the weight per cubic foot by G, 
the pressure per square foot in the vessel from which the flow 

* See Peabody's Thermodynamics, p. 132; also, art. " Hydromechanics," 
Encyc. Britannica. 



g6 



EXPERIMENTAL ENGINEERING. 



[§ 226. 



takes place by p lt the pressure against which the flow takes 
place by p 2 , the volume of one pound in cuLic feet by C, the 
absolute temperature corresponding to pressure/, by T lf the 
ratio of specific heats by y. 



2g 



y — U K \p x i 



H^l'Wh w 



also, 



T, 



T m 



and 



g x t~g<t; 



(30) 



226. Flow of Air. — For air, p = 21 16.8, £ = 0.08075, 
7^ = 492.6 at 32 Fahr., ^ = 1.405. Inserting these numerical 
values, we have the following equation for the theoretical 
velocity of flow of air through an orifice: 

Volume of Air discharged. — The volume of air discharged, 
in cubic feet per second at pressure of discharge, is to be com- 
puted by multiplying the area of the orifice F x in square feet, by 
the velocity v^ , by a coefficient of discharge c. Then 



Q* = cF x v % =cF x yJ 18: 

= 108.7^ 



/ 



\0.29 ) * 

) ! 



VM>-(f }■ ■<*> 



Substituting numerical values for the ratio of p^ to />, , we 
have 

&= 108.7^^0.16957; (33) 



* See article " Hydromechanics," Encyc. Britannica, Vol. XII, page 48] 



§ 227.] MEASUREMENT OF LIQUIDS AND GASES. 



297 



To express this in terms of the volume discharged from the 
reservoir Q l , in which p x is reservoir pressure and p 2 pressure 
of discharge, we have 

a = (£)'&. 



Substituting numerical values for free flow, 



a = (o.s2 7 y- m Q, = 0.6339a-, 



ft=io8.7^(J)y^{i-(^ 29 }. . . (34) 

Substituting values of p t -f-/,, 

Q, = 68.8^ V^ri^T, (35) 

227. Velocity of Flow of Air through an Orifice. — The 

velocity of flow is obtained by substituting numerical values in 
the preceding equations. We have, denoting by T x the abso- 
lute temperature in the reservoir as the greatest velocity of 
flow of air, 



£=183.6 7x1-0.8305). 



(36) 



Solving equation (36), we have the following theoretical 
results : 



Temperature of Air in Reservoir. 


1 Velocity of 
Flow in Feet 






Degrees Fahr. 


Absolute. 


per Sec. 


32 


492.6 


991 


70 


530.6 


1030 


IOO 


560.6 


IO58 


I50 


610.6 


1 105 


200 


660.6 


II48 


300 


760.6 


1233 


400 


860.6 


1312 


500 


960.6 


1386 



298 EXPERIMENTAL ENGINEERING. [§ 228. 

228. The Weight of Air discharged. — This is to be com- 
puted by multiplying the volume of discharge by the specific 
weight. 

Thus the weight of air is 

P 

G. = l -^ pounds per cubic foot, 



when /, and T x are, respectively, pressure and absolute tem- 
perature in the reservoir. Hence the weight of air dis- 
charged is 



W y 



[ = Q 1 G 1 =ioS. 7 cF 1 G 1 [p^T i (i-(jJ' 2 \ . ( 37 ) 



Weisbach has found the following values of c, the coefficient 
of discharge : 

Conoidal mouth-piece of the form of the con- 
tracted vein, with effective pressures of 

0.23 to 1.1 atmospheres 0.97 to 0.99 

Circular sharp-edged orifices 0.563 to 0.788 

Short cylindrical mouth-pieces 0.81 to 0.84 

The same rounded at the inner end 0.92 to 0.93 

Conical converging mouth-pieces „ . .... 0.90 to 0.99 

In the general formula for the flow of air, the weight de- 
livered becomes a maximum when 



A / 2 \ y-x 

A V + " " 

This equals 0.527 for air and 0.58 for dry steam. This has 
been verified by experiment, and tends to prove that the press- 
ure of the orifice of discharge is independent of the back- 
pressure. In the flow of air from a higher to a lower pressure 



§ 229.] MEASUREMENT OF LIQUIDS AND GASES. 299 

through a small tube or orifice, the pressure in the orifice may 
be less than the back-pressure. 

229. Flow of Air in Pipes. — When air flows through a long 
pipe, a great part of the work is expended in overcoming fric- 
tional resistances. This friction generates heat, which is largely 
used in increasing the pressure in the pipes, the only loss being 
from radiation, which is small. 

The expansion then is isothermal, the heat generated by 
friction exactly neutralizing the heat due to work. 

For pipes of circular section, when d is the diameter, /the 
length, p Q the greater and ■ p x the less pressure, T the absolute 
temperature, C the coefficient of discharge, c p (= 53.15 foot-lbs.) 
the specific heat, we have the initial velocity 

- = W^l <3*> 

This may be reduced to 



«.= (i.i 3 i9-a 7 26^)y/^. 

It has been found from recent experiments that fair values 
of the coefficient are as follows : * 

C = 0.005(1+^ 

in ordinary pipes for velocities of 100 feet per second ; 

C = 0.002 8 (l + 4) 

for pipes as smooth as those at the St. Gothard Tunnel. 

__ — ■ — 

* See " Hydromechanics," Encyc. Britannica, Vol. XII, p. 491. 



300 EXPERIMENTAL ENGINEERING. [§ 230. 

Weight of air flowing per second in circular pipes in pounds 
is given by the equation 

=o.6nj/jg(A s -A')}- 
Approximately, 

^=(0.6916/. -o.4438/i)(^)*. • • • (39) 

230. Flow of Steam through an Orifice. — Velocity. — In 
this case, as in Article 226, the expansion is supposed to be 
adiabatic. 

Denote by A the reciprocal of the mechanical equivalent 
of one B. T. U. corresponding to the quantity 778 ; by x x the 
quality or percentage of dry vapor in the reservoir, corre- 
sponding to the pressure per sq. foot /, , and by x^ the quality 
in the tube, corresponding to pressure/, ; by r x the latent heat 
per pound in reservoir, r 2 the same in the tube ; T x and 7!, the 
respective absolute temperatures, 6 X and 3 the respective 
entropies of the liquids, c the specific heat of the liquid, q x and 
q^ the sensible heat of the liquid in reservoir and tube ; the 
reciprocal of the weight of a cubic foot of the liquid by cr. 
Then 

At? 

= X f x _ x%r% J r a x -q, + A cr(p i - / 3 ). . (40) 

x, can be determined from the relation expressed in the 
equation 

^ + 0, = ^+0, (4I) 






§ 230.] MEASUREMENT OF LIQUIDS AND GASES. 



301 



If no tables are at hand for 0, , its approximate value can be 
deduced, since 



T t 



e x - # 2 = c log, T 

1 8 



(42) 



So that 



---■= -5F" + * log, =-. 



Eliminating x^ in equations (40) and (41), 



Av 2 _x l r 1 

IF" 



(r a -r s )- T^-^+C^-^ + ^fo-A). (43) 



The following table, condensed from Peabody's steam 
tables, gives the value of the entropy of the liquid : 

TABLE OF ENTROPY OF THE LIQUID. 



Absolute 


Entropy 


Absolute 


Entropy 


Steam- 


of the 


Steam- 


of the 


pressuret 


Liquid, 


pressure, 


Liquid, 


P 





P 





I 


O.1329 


65 


0.4337 


IO 


O.2842 


70 


O.4402 


15 


0.3I43 


75 


O.4464 


20 


O.3363 


80 


O.4522 


25 


0.3539 


85 


0.4579 


. 30 


O.3685 


90 


O.4633 


35 


O.38H 


95 


O.4686 


40 


O.3921 


100 


0.4733 


45 


O.4020 


105 


O.4780 


50 


O.4109 


no 


O.4826 


55 


O.419I 


115 


O.4869 


60 


O.4267 


120 


0.4911 



In the above equations^ has a numerical value of I -r- 778, 
a is nearly equal to 0.016, g to 32. 16. 



* See Thermodynamics, by Peabody, page 138. 



302 EXPERIMENTAL ENGINEERING. [_§ 2 3 2 - 

It has been shown that in the flow of saturated steam p 
will not fall below 0.58 of p lt because at that point there is the 
maximum weight of discharge. In the actual trials this seems 
to be nearer 0.61 than 0.58. If we assume p a equal to 0.6/ , , 
the velocity will be found to be nearly constant, and to vary 
but little from 1400 feet per second. 

231. Weight of Steam discharged through an Orifice. 
— This was determined experimentally by R. D. Napier, and 
expressed by the formula 

70' 

in which W= weight discharged in pounds per second, F — 
area of orifice in square inches, and/, is the absolute pressure 
of the steam, pounds per square inch, which is equal to or 
greater than if that of the atmosphere. 

This formula has been verified by experiments made in the 
Laboratories of Sibley College and also at the Massachusetts 
Institute of Technology, and is found to vary but little from 
the actual results. 

232. Measurement of the Flow of Gas. — Gas-meters. — 
In the measurement of gas the product of absolute pressure, 
p, by volume, v, divided by absolute temperature, T, is a con- 
stant quantity. Thus 

pv p x v x 
Y == ~7\' 

If p and T can be kept constant, the quantity discharged 
will vary as the volume ; \i p and T are known, the quantity dis- 
charged can be computed. 

Gas-meters are instruments for measuring the volume of 
gas passing them. They are constructed on various plans and 
are known as Wet or Dry, depending on whether water is used. 
The volume is usually measured in cubic feet. 

Meter-prover. — This is the name given to a sort of gasometer 
arranged as shown in Fig. 147. It consists of an open vessel. 



§ 232.J MEASUREMENT OF LIQUIDS AND GASES. 



303 



BE, partly filled with water, into which a vessel, AF, of some- 
what smaller diameter is inverted. The weight of the vessel AF 
is counterbalanced by a weight W which descends into a vessel 
of water CK at such a rate as to keep the sum of the displace- 
ments of the two vessels constant, in which case the pressure 




Fig. 



on the confined gas in the vessel AF will remain constant. 
The gas flows out through the pipe T, its pressure being taken 
by a manometer at m, its temperature by a thermometer at t. 

Fig. 148 shows a form of meter-prover made by the Ameri- 
can Meter Co., in which the counterweight lifts an additional 
weight moving over an involute wheel, so calculated that the 
pressure on the outflowing gas remains constant. These instru- 
ments are used principally to calibrate meters ; they give very 
accurate results, but are not suited for continuous measure- 
ments. 

Wet-meter. — The wet-meter works on the same principle as 
the meter-prover, but is arranged with a series of chambers 



304 



EXPERIMENTAL ENGINEERING. 



[§ 232. 



which are alternately filled and emptied with gas. These 
chambers are usually arranged like an Archimedean screw, as 
shown in section in Fig. 149. 




Fig. 148.— Meter-prover. 

Gas is admitted just above the surface of the water, and 
raises the partition of the chamber, bringing it above the water 
and filling it. The outlet-pipe is submerged until the chamber 
is filled. It is connected with the case of the meter, as shown 
in the figure. The gas is completely expelled as the cylinder 
revolves. 



§ 232. J MEASUREMENT OF LIQUIDS AND GASES. 305 

The wet-meter is a very accurate measure of the gas pass- 
ing, provided the water-level be maintained at the constant 
standard height. Any change of the water-level changes the 
size of the chambers accordingly. The motion of the cylinder 
actuates the recording mechanism. 



Fig 149.— The Wet-meter. 

The Dry Gas-meter. — The dry gas-meter possesses the ad- 
vantage of not being affected by frost, nor of increasing the 
amount of moisture in the gas. The dry-meter is made in vari- 
ous forms, and generally consists of two chambers separated 
from each other by partitions. Each chamber is divided into 
two parts by a flexible partition which moves backwards and 
forwards, and actuates the recording mechanism as the gas 
flows in or out. This motion is regulated by valves somewhat 
similar to those of a steam-engine. The gas-meter is calibrated 
by comparing with . a meter-pro ver as already described. 
These meters are not supposed to be instruments of great 
accuracy. 



306 



EXPERIMENTAL ENGINEERING. 



L§ 233. 



233. Anemometers.— Instruments that are used to measure 
the velocity of gases directly are termed anemometers. They 
consist of flat or hemispherical vanes mounted like arms of a 
light wheel so as to revolve easily. The motion of the wheel 
actuates a recording mechanism. Robinson's Anemometer, 
which consists of hemispherical cups revolving around a vertical 
axis, is much used for meteorological observations. 

A form shown in Fig. 150 with flat vanes, and with the 




Fig. 150. — Biram's Portable Anemometer. 



dial arranged in the centre as shown, or on top of the case in 
various positions, is much used as a portable instrument. 

The dial mechanism of the anemometer can be started or 
stopped by a trip arranged convenient to the operator ; in some 
instances the dial mechanism is operated by an electric current 
similar to that described in connection with the tachometer, 
Article 221, page 262. It is also made self-recording, by attach- 
ing clock-work carrying an endless paper strip which is moved 
under a pencil operated by the anemometer mechanism. 



§ 234-J MEASUREMENT OF LIQUIDS AND GASES. 307 

234. Calibration of Anemometers. — Anemometers are 
calibrated by moving them at a constant velocity through still air 
and noting the readings on the dials for various positions. This 
is usually done by mounting the anemometer rigidly on a long 
horizontal arm which can be rotated about a vertical axis at a 
constant speed. The distance moved by the anemometer in 
a given time is computed from the known distance to the axis 
and the number of revolutions per minute ; from these data 
the velocity is computed. 

In performing this experiment care must be taken that the 
axis of the anemometer is at right angles to the rotating arm. 
Readings should be taken at various speeds, since the correc- 
tion is seldom either a constant quantity or one directly de- 
pendent on the velocity. 

The Anemometer can also be calibrated by computing the 
heating effect due to the condensation of a given amount of 
steam. The method of calibration would be as follows: pass 
the air through a tube or box containing a coil of steam-pipe 
sufficient to warm the air sensibly, say 20 or 30 degrees. 
Measure the quality of the entering steam and the amount of 
condensation, and from that compute number of heat-units 
taken up by the air. Guard against all loss of heat by the 
air; then this last quantity becomes evidently equal to the 
increase in temperature of the air multiplied by its specific 
heat, multiplied by its weight. From this computation the 
weight of the air can be computed. Knowing the weight of 
air and its temperature, compute the volume flowing in a given 
time, divide this result by the area of the cross-section, and 
obtain the velocity. This method is likely to give more 
satisfactory results than that of swinging the dynamometer in 
the air. Also see Chapter XXIV, Art. 490. 



CHAPTER IX. 
HYDRAULIC MACHINERY. 

235. General Classification. — Hydraulic machinery may 
be divided into the two classes, hydraulic motors and pumps. 
In the first class a quantity of water descending from a higher 
to a lower level, or from a higher to a lower pressure, drives a 
machine which receives energy from the water. In the latter 
class a machine driven by some external source of energy is 
employed in lifting water from a lower to a higher level. 

The student is advised to consult the following authorities 
on the subject : 

Rankine's Steam-engine ; article " Hydromechanics," En- 
cyc. Britannica ; Weisbach's Mechanics, Vol. II. (Hydraulics); 
" Systematic Turbine-testing," by Prof. Thurston, Vol. VIII. 
Transactions Mechanical Engineers ; " Notes on Hydraulic 
Motors," by Prof. T. P. Church. 

236. Hydraulic Motors — Classification. — The following 
classes of hydraulic motors are usually recognized : 

I. Water-bucket Engines, in which water poured into sus- 
pended buckets causes them to descend vertically, so as to lift 
loads and overcome resistances. 

II. Water-pressure Engines, in which water by its pressure 
drives a piston backward and forward. 

III. Vertical Water-wheels, in which the water acts by 
weight and impulse to rotate them on a horizontal axis. 

IV. Turbines, in which the water acts by pressure and im- 
pulse to rotate them around a vertical axis. 

V. Rams and Jet-pumps, in which the impulse of one mass 
of fluid is used to drive another. 

308 



§239-] H YDFA ULIC MA CHINER V. 3 09 

237. Energy of Falling Water. — Hydraulic motors are 
driven either by the weight, pressure, or impulse of moving 
water. Neglecting the losses due to friction or other causes, 
the energy of falling water is the same whether it act by (I.) 
weight, (II.) by pressure, or (III.) by impulse. This is proved 
as follows : 

Let h equal the head or total height of fall, Q the discharge in 
cubic feet per second, G the weight per cubic foot,/ the pressure 
in pounds per square foot, v the velocity in feet per second, P 
the pressure in pounds per square inch. Since the work done 
is equal to the product of the force acting into the space moved 
through, we have for the work done per second in the several 

cases (I.) GQh, (II.) (pQ), (III.) GQ— ; but since p = Gh and 
h = — , we have by substitution 

GQk=pQ=GQ~ = i44PQ^ .... (I.) 

238. Parts of an Hydraulic Power- system. — The hydrau- 
lic power-system in general requires — 

1. A supply-channel or tube leading the water from the 
highest accessible level. 

2. A discharge-pipe or tail-race conveying the water away 
from the motor. 

3. Gates or valves in the supply-channel, and a waste-chan- 
nel or weir to convey surplus water away from the motor. 

4. The motor, which may belong to any of the classes de- 
scribed in Article 236, and suitable machinery for transmitting 
the energy received from the motor to a place where it can be 
usefully applied. 

239. Water-pressure Engines.* — Water-pressure engines 
are well adapted for use where a slow motion is required and a 
great pressure is accessible. 

* See Weisbach's Hydraulics, Vol. II, p. 558. 






3io 



EXPERIMENTAL ENGINEERING. 



[§ 2 4 0. 



These engines resemble in many respects a steam-engine, 
water being the motive force instead of steam. They consist 
of a cylinder (Fig. 151) in which a piston T is worked alter- 




Fig. 15T.— Water-pressure Engine. 



nately forward and backward, water being admitted alternately 
at the two ends of the cylinder by the moving slide-valve 6". 
While water is passing into one end of the cylinder through 
the passages D> E, C, it is being discharged through the pipe 
E t G t H, which is proportioned so as to afford a free exit to 
the water. Near the end of the stroke of the piston the slide- 
valve S closes both admission-ports, and the pressure in the 
cylinder C x is increased by the diminution of volume caused 
by the motion of the piston. When the pressure in the cham- 
ber C x exceeds that in the supply-pipe the valve W x opens, 
and the water passes into the supply. Simultaneously the 
valve Fis opened by suction, and water passes into the cham- 
ber C from the discharge-pipe. The effect of this action is to 
gradually arrest the motion of the piston at the end of the 
stroke by reducing the pressure on one side and increasing the 
resistance on the other. When the piston reaches the end of 
the stroke the slide-valve is reversed in position and a new 
stroke is commenced. 

240. Vertical Water-wheels. — There are four classes of 
vertical water-wheels : 

I. Overshot, in which the water is received on the top of 



§241.] 



HYDRA ULIC MA CHINE R Y. 



3" 



the wheel and discharged at the bottom, the water acting prin- 
cipally by weight. 

2. Breast, in which the water is received on the side of the 
wheel and held in place by a guide or breast, the water acting 
both by impact and weight. 

3. Undershot, in which the water acts only on the under 
side of the wheel, the water acting principally by impact. 

4. Impact, in which the water is delivered to the wheel 
by a nozzle, acting generally on the top or bottom, and by im- 
pulse only. 

241. Overshot Water-wheels. — The overshot water-wheel 
shown in section in Fig. 152 is well adapted to falls between 10 
and 70 feet and to a water- 



supply of from 3 to 25 cubic 
feet per minute. On the 
outside of the wheel is built 
a series of buckets, which 
should be of such a form as 
to receive the water near the 
top at D without spilling or 
splashing, to retain the water 
until near the bottom, and to 
empty completely at the bot- 
tom. The number of buckets 
must be such that there shall 
be no spilling by overflow at 
the top. The head of water 
above the wheel must be sufficient to give the falling water 
greater velocity than the periphery. The peripheral velocity 
in practice is from 5 to 10 feet per second, that of the falling 
water from 9 to 12 feet per second, corresponding to a height 
of from 16 to 27 inches above the wheel. 

These wheels are not adapted to run in back water, and 
have the greatest efficiency for a given head when revolving 
just free from the discharged water. 

The principal formulae relating to the overshot-wheel are as 
follows : 




Fig. 152. — Section of Overshot Water- 
wheel. 






3 I2 



EXPERIMENTAL ENGINEERING. 



[§ 2 4 I. 



Let d equal the depth of the buckets, b the width of the 
wheel, r the radius of the wheel, n the number of revolutions 
per second, v the peripheral velocity in feet per second, Q the 
water-supply in cubic feet per second, Q x the capacity of that 
part of the wheel that passes in one second, m the ratio of the 
water actually carried to the capacity of the buckets — m being 
usually about one fourth — .AT the number of buckets. 




Fig. 153.— Section of Breast-wheel. 

Then, supposing the wheel to be set just free of the back 
water, 

h = 2r -\- (i-J- to 2) all in feet ; 

27ZT 

N = —j- = , usually, or ; 



bv 
Q 1 = —{2rd— d*) = bdv, nearly; 



Q — mQ, —rnbdv ; 
v = 2nnr. 



§ 243-] HYDRA ULIC MA CHINE R Y. 3 I 3 

The efficiency is the ratio of the work delivered to the en- 
ergy received from the falling water. 

The efficiency of the best wheels of this class reaches 75 
per cent. 

242. Breast-wheels. — The form of breast-wheel is shown 
in Fig. 153. The water is received at a height slightly above or 
below the centre C of the wheel, and is prevented from falling 
away from the wheel by the curved breast ABB; the water 
acts on the radial or .slightly curved buckets, thus tending to 
revolve the wheel partly by weight and partly by impulse. 

The flow of water is regulated by a gate at 5. 

The formulae applying to breast-wheels are essentially the 
same as those for overshot-wheels. The efficiency of the best 
wheels of this class varies from 58 to 62 per cent. 

243. Undershot-wheels. — The undershot-wheel differs 
from the breast-wheel in receiving the water at or near the 
bottom ; the water flows in a guide under the wheel, which guide 
in some cases extends some dis- 
tance up the sides. The usual form 
of such wheels is shown in Fig. 
154; the buckets or floats are often 
radial, sometimes, however, of con- 
cave or bent form. 

If we let c equal the velocity of 
water as it strikes the wheel, v the 
peripheral velocity of the wheel, Q 
the quantity of water in cubic feet FlG - 154.— Undershot-wheel. 
per second, G the weight per cubic foot, k 2 the portion of the 
head corresponding to the elevation of the entering water as it 
strikes the wheel over that of the discharge, P the force de- 
livered at the circumference of the wheel ; then will the effi- 
ciency rf be obtained by the following formulae :* 

Pv 

Tf=z 




&[£=&+$ 



* See Weisbach's Hydraulics, page 291. 



314 EXPERIMENTAL ENGINEERING. [§244 

From experiments of Morin it was found that when v -r- c 
was less than 0.63, the efficiency 7 was 0.41. When v -7- c was 
between 0.63 and 0.8, rf was 0.33. The efficiency obtained 
from the best form of these wheels is O.55. 

Poncelefs Wheel. — When the floats of the undershot wheel 
are curved in such a manner that the entering jet of water is 
allowed to flow along the concave sides and press against them 
without causing shock, a greater effect is obtained than when 
the water strikes more or less perpendicularly against plane 
floats. Such wheels are called, after their inventor, Poncelet 
wheels. The efficiency of such wheels in some instances has 
reached 68 per cent. 

244. Impulse-wheels. — In this class of wheels several jets 
of water impinge on the buckets of the wheel as they are 
successively brought into position by the rotation. This class 
is very efficient for high heads and a small supply of water. 
The efficiency to be obtained by the action of a jet of water 
on a moving bucket is fully discussed in Vol. II., Church's 
" Mechanics of Engineering," page 808. 

Denote by c velocity of the jet, v the peripheral velocity of 
the vane, ex the angle of total deviation relatively to the vane 
of the stream leaving the vane from its original direction, G 
the weight per cubic foot of water, F the area of the stream, 
Q the volume of flow per unit of time over the vane. The 
work done per unit of time, 

OC 
L = Pv = —-(c — v)v[i — cos a], 

o 

This is maximum when v — \c. 

In case a hemispherical vane is used, a will equal 180 , and 
1 — cos a = 2. For that case, a == 180 and v = \c> we have 

L=Z QG t_ 

g ' *' 

In case the absolute velocity of the particles leaving the 
vane equal zero, an efficiency equal to unity would be possible. 



§ 245-] 



HYDRA ULIC MA CHINE R Y 



315 



One or more jets of water are used as necessary to produce 
the maximum power. Fig. 155 shows the Pelton wheel, provided 
with four jets. The bucket of this wheel shown at B is of double 
hemispherical form with a sharp midriff, separating the two parts, 
which splits the jet and turns each part through an angle of 
180 . The efficiency of is wheel has in some instances ex- 
ceeded 80 per cent. 




Fig. 155. — The Pelton Impulse-wheel with Four Jets. 



There is a large number of motors in this class, some of 
which are adapted for high heads and large powers. The Doble 
wheel is provided with a needle regulating- valve controlled by 
the governor. The Cascade has buckets arranged on each side of 
the wheel, the edge of the wheel serving to divide the jet. Most 
of the small hydraulic motors are of impulse type. 

245. Turbines. — The turbine-wheels receive water con- 
stantly and uniformly, and usually in each bucket simultane- 
ously. The buckets are usually curved, and the water is guided 
into the buckets by fixed plates. The name was originally 
applied in France to any wheel rotating in a horizontal plane, 
but the wheels are now frequently erected so as to revolve in 
vertical planes. The turbine was invented by Fourneyron in 
1823, the original wheel being constructed to receive water near 



3l6 EXPERIMENTAL ENGINEERING. [§246. 

the axis, and to deliver it by flow outward at the circumfer- 
ence. Turbines are now built for water flowing parallel to the 
axis, and also inward from the circumference toward the 
centre ; they are also constructed double and compound. In 
some of the turbines the wheel-passages or buckets are com 
pletely filled with water, in others the passages are only partly 
filled. 

The following classes are usually recognized : 
I. Impulse Turbines. 

II. Reaction Turbines. 

In both these classes the flow may be axial outward, in- 
ward, or mixed, and the turbine may be in each case simple, 
double, or compound. 

In the Impulse turbines the whole available energy of the 
water is converted into kinetic energy before it acts on the mov- 
ing part of the turbine. In these wheels the passages are never 
entirely filled with water. To insure this condition they must be 
placed a little above the tail-water and discharge into free air. 

In the Reaction turbines a part only of the available energy 
of the water is converted into kinetic energy before it acts on 
the turbine. In this class of wheels the pressure is greater at 
the inlet than at the outlet end of the wheel-passages. The 
wheel-passages are entirely filled with water, and the wheel may 
be, and is generally, placed below the water-level in the tail-race. 

246. Theory of the Turbine. * — The water flowing through 
a turbine enters at the admission-surface and leaves at the dis- 
charge-surface of the wheel, with its angular momentum rela- 
tive to the wheel changed. It must exert a couple —M, tend- 
ing to rotate the wheel, and equal and opposite to the couple 
M which the wheel exerts on the water. Let Q cubic feet enter 
and leave the wheel per second, c x , c 2 be the tangential com- 
ponents of the velocity of the water at the receiving and dis- 
charging surfaces of the wheel, r 1 , r 2 the radii of these surfaces. 
Then 

-if=^(v.— vj (1) 

g_ 

* See " Hydromechanics, " Encyc. Britannica. 



§ 246. J H YDRA ULIC MA CHINER Y. 3 I 7 

If a is the angular velocity of the wheel, the work done on 
the wheel is 

GO 
T = Ma = — — (c x r i — c^r^a foot-pounds per second. (2) 

The total head of the water h t is reduced by friction and 
resistances h p in the channels leading to the wheel, so that 
the effective head h which should be used in calculating the 
efficiency is 

h — h t — h p (3) 

In case the construction of the turbine requires that it set 
above tail-race d feet, the velocity of water in the turbine 
should be calculated for a head of h— d, but the efficiency for 
a head of h feet. The work of the turbine is partially absorbed 
in friction. 

Let T equal the total work, T d the useful work, and T t the 
work used in friction. Then 

T=T d +T t (4) 

The gross efficiency 

'=A" • • ; « 



The hydraulic efficiency 



n= m (6 > 



The hydraulic efficiency is of principal importance in the 
theory of turbines. Substituting this value of T in equation (2), 

far, — cs^a 

. 1- g k ' (7 > 

which is the fundamental equation in the theory of turbines. 



318 EXPERIMENTAL ENGINEERING. [§247. 

For greatest efficiency the velocity of the water leaving 
should be o, in which case c t = o and 

C T SY 

V = ^- ....... (8) 

But r t a is the lineal velocity of the wheel at the inlet surface ; 
if we call this V x , 

V= C 4r (9) 



The efficiency of the best turbines is 0.80 to 0.90. 

Speed of the Wheel. — The best speed of the wheel depends 
on frictional losses which have been neglected in the preced- 
ing formulae. The best values are the ones obtained by ex- 
periment. Let V equal the peripheral velocity at outlet, V { 
at inlet, r and r t the corresponding radii of outlet and inlet 
surfaces. Then we shall have as best speeds* for 



axial-flow turbine V — V t = 0.6 V2gk to 0.66 V2gh ; 



radial outward-flow turbine V t = 0.56 \2gh; V = FJ 



r n 



r n 



radial inward-flow turbine V t = 0.66 V2gh ; V = V t - . 



247. Forms of Turbines. — Fourneyron s Turbine. — This is 
an outward-flow turbine, with a horizontal section as shown in 
Fig. 156. C is the axis of the wheel, which is protected 
irom the water by vertical concentric tubes shown in section. 
On the same level with the wheel and supported by these 
tubes is a fixed cylinder, with a bottom but no top, contain- 
ing the curved guides F F. The wheel AA is supplied with 
curved buckets bd, b x d x , so arranged as to absorb most of the 
energy of the water; the water enters the wheel at -the inner 
edges of the buckets and is discharged at the outer circum- 

* " Hydromechanics " Encyc. Britannica. 



§ 2 4 8.] 



HYDRAULIC MACHINERY. 



319 



ference. Gates for regulating the supply of water are shown in 
section between the ends of the guides and the wheel. 




Fig. 156.— Outward-flow Turbine. 

248. Reaction - wheels. — The simple reaction-wheel is 
shown in Fig. 157, from which it is seen to consist of a vertical 
cylinder, CB, which receives the water, and two cylindric arms, 
G and F\ on opposite sides of each 
arm is a circular orifice through which 
the water is discharged. The effect 
of this arrangement is to reduce the 
pressure on the sides toward the ori- 
fices, thus producing an unbalanced 
pressure which tends to make the 
wheel revolve. If we denote by h the 
available fall measured from the level 
of the water in the vertical pipe to the B|j||j§|j 
centre of the orifices, r the radius of Bl 



rotation measured from the axis to the FlG - 157.-THE Reaction-wheel. 
centre of each orifice, v the velocity of discharge, a the angular 
velocity of the machine, F the area of the orifices, — when at 
rest the velocity would equal ¥2gh, but when in motion the 
water in the arms moves with a velocity ar, which corresponds 
to an increased head due to centrifugal force of arV -+- 2g. 




320 



EXPERIMENTAL ENGINEERING. 



[§ 2 4 8. 



Hence the velocity of discharge through the orifices is 



v = V2gh + tfV 2 ; 



/he quantity discharged 



FV2gk + a i r\ 



Since the orifices move with a velocity ar, the velocity with 
reference to a fixed point is v — ar. 

If G be the weight per cubic foot, the momentum or mass 
times the velocity is 

— (v — ar) 
g 

This mass moves with an angular velocity a and arm r, hence 
the work done per second in rotating the wheel is 

CO 

(v — ar)ar foot-pounds. 

The work expended by the water-fall is GQk. 
Hence the efficiency 



p = 



(v — ar\ar 



gh 



This increases as ar increases, or the maximum efficiency is 
reached when the velocity is infinite. The friction considera- 
bly reduces these results, and experiment indicates the greatest 
efficiency when ar = V2gk. In which 
case, by substitution, we should have 
rf = 0.828. 

The best efficiency realized in prac- 
tice with these wheels is about 0.60. 

The Scottish turbine, shown in Pip - , 

1 16 in section, is a reaction-wheel with 

Fig, 158.— Scottish Turbine, three discharge-jets, the water being 

supplied from a tube filled with water under pressure beneath 

the wheel. 




$ 2 49-] 



HYDRAULIC MACHINERY. 



321 



249. The Hydraulic Ram. — The hydraulic ram is a ma- 
chine so arranged that a quantity of water falling a height k 
forces a smaller quantity through a greater height h\ 




2 - > 



Fig. T59.— Hydraulic Ram. 



The essential parts of the hydraulic ram are: I. The air- 
chamber C, connected with the discharge-pipe eD, and pro- 
vided with a clack or check-valve 0, opening into the chamber 
C from the pipe ss. 

2. The waste-valve, Bd, is a weighted clack or check- 
valve, opening inward and connected to a stem df\ on the 
stem is a nut or cotter at f to regulate the length of stroke, i.e., 
amount of opening of the waste-valve. 

3. The supply-pipe ss, that leads to a reservoir from which 
the supply is derived, should be of considerable length. If it is 
very short when laid in a straight line, bends must be made to 
secure additional length, and also to present some resistance to 
the backward wave-motion ; its length must not be less than 
five times the supply-head. The working parts of the ram are 
the check-valve o and the waste-valve dB ; these parts move 
in opposite directions, and alternately. 

The action of the ram is explained as follows : 



322 EXPERIMENTAL ENGINEERING. [§ 250. 

Water is supplied the ram by the pipe ss ; the waste-valve 
dB being open, the water escapes with a velocity due to the 
height h. The water escaping at <^ suddenly closes the waste- 
valve. The acquired momentum of the moving column of 
water in the pipe ss is sufficient to raise the valve and dis- 
charge a portion of its weight to a height k '. As soon as the 
pressure is reduced the valve closes, the waste-valve dB opens 
and the water again flows down the pipe ss. These motions 
are produced with regularity, and the water acquires a backward 
and forward wave-motion in the pipe ss. A small air-chamber 
at/, with a small check-valve opening inward at c to supply the 
chamber with air, are found to add to its efficiency. 

The wave-motion has been utilized to operate a piston back- 
ward and forward beyond the waste-valve, the piston being 
utilized as a pump in raising water from a different supply. 

Formnlce. — Let h equal the height of the reservoir above 
the discharge-valve of the ram, h' the height to which the 
water is raised above reservoir, Q the total water supplied to 
the ram per second, q the amount raised to the height h! , G the 
weight per cubic foot. Then the useful work equals Gqh' ; the 
work which the water is capable of doing equals Gh(Q — q). 

The efficiency 

qh' 



V = 



(Q - q)Jl 



Rankine (see Steam-engine, page 212) gives the following 
formulae for obtaining the dimensions of a ram : 

Let L equal length of supply-pipe, D the diameter of 
supply-pipe in feet ; other symbols as above. Then 

2h' 



D = V1.63Q, L = h + ti + -p 

Volume of air-chamber C equals volume of feed-pipe. 
250. Methods of Testing Water-motors. — The methods 
of testing hydraulic motors require in all cases the measure- 



§ 250.] HYDRA ULIC MA CHINER Y. 323 

ment (1) of volume or weight of the water discharged, (2) of 
the net head, or pressure acting on the motor, or (3) the 
velocity of discharge. From these measurements may be com- 
puted the energy received by the motor, by the formulas 
already given. 

1. Measurement of the Water may be made in the case of 
small motors by receiving the discharge in tanks standing on 
scales ; two tanks will be required, one of which is filling while 
the other is emptying. Temperature observations must be 
taken, and from the known weight and temperature the volume 
(<2) may be computed, if required. The tanks may be previ- 
ously calibrated by filling to a known point, and be so con- 
nected that any excess will pass into the tank recently emptied, 
in which case a method similar to the above may be used with- 
out scales. 

The measurement will usually have to be made by discharg- 
ing over weirs (see page 2 74) or through nozzles or Venturi tubes; 
this will be especially true for large motors. 

With water-pressure engines an approximate measurement 
may be made by the piston-displacement, corrected for slip. 
A discussion of the effect of slip is to be found on page 302. 

2. Measurement of the Head (h) may be made, in the first 
place, by taking a series of levels from standing water in the 
tank or dam above, to the level of the water in the tail-race. 
This measurement must be corrected for loss of head by fric- 
tion in the pipes, or by flowing over obstructions, etc., this at 
best can be made only in an approximate manner. To secure 
the full effects of the head, some turbine-wheels are set with 
draught or suction tubes leading from the wheel to the water- 
level in the tail-race ; this will not affect the method of measur- 
ing the head. The head acting on the wheel is measured most 
accurately by a calibrated pressure-gauge, placed in the supply- 
pipe near the motor. The reading of this gauge if merely at- 
tached to the supply-pipe in the usual manner, would be that 
due to the pressure-head only, and would be less than the true 
head acting on the pipe. By inserting a tube well into the 
current, and bent so as to face the current, thus forming a Pitot 



324 EXPERIMENTAL ENGINEERING. [§ 2 5l» 

tube (Article 222, page 292), the pressure will be increased the 
amount due to the velocity-head, and the gauge if attached to 
this tube will give the pressure corresponding to the actual head. 
To the head so obtained must be added the distance from the 
centre of the gauge to the level of the water in the tail-race. 
In case the draught-tube is used, a vacuum gauge or mercury 
manometer can be attached, and the suction-head calculated 
from the gauge-reading may be compared with the measured 
distance. In case two gauges are used, the vertical distance 
between them must be measured, and considered a portion of 
the head. 

To obtain the head corresponding to a given pressure, in 
pounds per square inch, multiply the gauge-reading by the 
height, in feet, of water corresponding to one pound of pressure. 

One pound of pressure per* square inch corresponds to 
2.308, 2.309, 2.31, 2.312, 2.315, 2.319, and 2.32 feet of head of 
water at the temperatures of 40 , 50 , 6o°, yo°, 8o°, 90 , and 
ioo° F., respectively. 

The head of one inch of mercury corresponds to 1.13 feet 
of water a_ ;\r>° F. 

Knowing che quantity or weight of discharge and the head, 
the energy received may be computed by any one of the four 
forms in equation (1), Article 237, p. 309. 

3. The velocity of discharge can seldom be measured directly \ 
it can be computed from measures of the pressure or net head,, 
since the velocity V = V2gh. It is rarely of importance. 

In case the motor is supplied with water through a nozzle, 
its least area may be determined by measurement ; then the 
quantity discharged may be computed as the product of ve- 
locity, least area, and coefficient. (See Article 204, p. 275.) 

251. Special Tests. — Backus or Pelton Motors. — Apparatus 
needed. — Pressure-gauges, two receiving tanks on scales or small 
w r eirs, Prony brake, pipes to remove water, thermometer. 

Testing Directions. — Measure nozzle ; note its position and 
the angle at which jet will strike buckets ; attach pressure- 
gauge, and arrange to measure discharged water ; attach Prony 
brake. Vary the head of water by throttling the supply ; if 



§251.] H YDRA ULIC MA CHINER V. 325 

heads are required greater than will be given by the water-works 
pressure, they must be supplied by pumping with a steam- 
pump. Take four runs of one half-hour each, with heads 
varying by one fourth, the greatest to be attained. Obtain 
corrections to head for position of gauge. Make running 
start. Take observations once in five minutes of water dis- 
charged, temperature, gauge-readings, weight on Prony brake- 
arm, and number of revolutions. 

In report, describe motor, with dimensions, method of test- 
ing; compute energy received in foot-pounds per minute and 
in horse-power ; compute work done in the same units ; compute 
efficiency of each run, also for varying velocity of perimeter. 

Make a plot on cross-section papef, with work delivered in 
foot-pounds per minute as abscissae, and heads as ordinates. 
Compare theoretical with actual efficiency. 

Turbine Water-wheels. — Large weirs must be arranged 
with which the discharged water can be measured. A Prony 
brake is to be arranged to absorb the power from the wheel, 
or a large transmitting dynamometer may be provided to 
receive the power developed by the wheel. Measurements to 
be made as explained in Article 250. 

Water-pressure Engines are to be tested essentially as 
described for the hydraulic ram. When used to operate a 
pump, indicator-diagrams are to be taken from both engine and 
pump ends, as explained in the chapter on steam-engine testing. 
From these can be computed the energy received by the pistons 
of the water-engine and that delivered from the piston of the 
pump. The quantity of water received will have to be meas- 
ured independently. 

Hydraulic Ram. — Apparattis ' as before, with additional 
pressure-gauge for discharge-pipe, means of measuring the 
water delivered and the water wasted. 

Testing. — Measure head of water acting on the ram and of 
that delivered as explained. Make runs of one half-hour 
each, with varying heads of supply and delivery. Take ob- 
servations once in five minutes of gauge on supply-pipe, on 



326 



EXPERIMEN TA L ENGINEERING. 



[§ 252. 



delivery-pipe, of weir-readings or weights of water wasted, and 
of water delivered. Compute the energy received and work 
done expressed in foot-pounds per minute, and also the effi- 
ciency for each run. 

In Report. — Describe the ram, method of testing, and draw 
a curve, with heads as ordinates and foot-pounds of work as 
abscissae. 

252. Forms for Tests of Hydraulic Motors. — The fol- 
lowing form for log and results has been used by the author : 



Efficiency test of Water-wheel. 

Type Rapacity 

At \ 

Date B n 

Length of Brake-arm. . . ... .ft. ; Weir zero 



Diam. 



Temp. Water °F. 



Q = 



DATA. 



£ = 



D. H. P . 

WXH 



X 33,ooo. 






Head on 
Wheel. 



Lbs. Ft 



Water used. 



Cu. ft. 
per sec. 



Lbs. per 
min. 



eta. 



D.H.P. 



2 c 

- V 
O l-i 



a o P.t! 



Form and dimensions of Buckets 

Number of Buckets Form of Delivery-tube 

Diameter 



The following form for test of the Swain turbine is used at 
the Massachusetts Institute of Technology : 



§ 2530 



No. 



HYDRAULIC MACHINERY. 

TEST ON SWAIN TURBINE. 
Date 



327 



188.. 





Time. 


Read- 
ing of 
Coun- 
ter. 


Revolu- 
tions 
per.... 
Minutes. 


Load 

on 
Brake. 


Height 

of 
Water 

in 
Tank. 


Height 

of 
Water 

Wheel- 
pit. 


Read- 
ing of 
Hook- 
gauge. 


f Hook- "If 
I gauge 1 
1 Read-f 
I ing- J 


Tem- 
pera- 
ture in 
Wheel- 
pit. 






















Total 















































































Diameter of wheel ft. Radius of brake ft. 

Crest of weir above floor of pit ft. 

Width of weir and pit ft. 

Correction for hook-gauge ft. 



Observed depth on weir (corrected). .ft. 

Total head acting on wheel ft. 

Weight of 1 cubic foot water at ° Fahr lbs. 

Revolutions of wheel per minute 

Quantity of water passing weir (uncorrected) cu. ft. 

" " " (corrected) cu. ft. 

Available work ft.-lbs. per sec. 

Work at brake ft.-lbs. per sec. 



Efficie 



,per cent. 



lency .... , 

H orse-power of wheel , 

Velocity due to head acting on wheel ft. per sec 

Velocity of outside of wheel ft. per sec 

Signed 



253. Classification of Pumps. — The different classes of 

pumps correspond almost exactly to the different classes of 

water-motors, with the mechanical principles of operation 
reversed. 



328 EXPERIMENTAL ENGINEERING. [§ 2 34. 

Ordinary reciprocating pumps correspond to water-engines; 
chain- and bucket-pumps, to water-wheels in which the water 
acts principally by weight. Scoop-wheels are similar to under- 
shot water-wheels, and centrifugal pumps to turbines. The 
various classes of pumps are as follows : 

A. Reciprocating, divided according to the method of con- 
struction into lift, force, combined lift and force, double-acting, 
and diaphragm. 

B. Rotary, divided into: (1) inferential, in which the water 
is urged forward by the velocity of the working parts of the 
pump, as in the centrifugal pump ; (2) positive, in which all 
the water that passes the pump is lifted or forced by the work- 
ing parts of the pump to a higher level ; the working parts of 
these pumps are usually gears or cams meshing together. 
These pumps are often spoken of as rotary, in distinction from 
centrifugal. 

Pumps are also classified by the power used to drive them. 
Thus, pumps driven directly by attached engines are termed 
steam pumping-engi?tes or steam-pumps; those driven from run- 
ning machinery by belts or gears are termed power-pumps; those 
operated by hand, hand-pumps. 

254. Duty and Capacity. — The term duty is applied to the 
work done by steam-pumps. This term originally signified the 
number of pounds of water lifted one foot by the consumption 
of one bushel (94 pounds) of coal ; more recently it has been 
the water lifted one foot by the consumption of 100 pounds of 
coal. It has, in recent tests, been customary to assume that 
each pound of coal evaporates ten pounds of water, from and 
at 212 , under atmospheric pressure. As each pound of water 
evaporated under such conditions requires 965.7 British thermal 
units,* and each B. T. U. is equivalent to 778 foot-pounds of 
work, a definite amount of work is done by 100 pounds of coal, 
equivalent to 965,700 B. T. U., or to 751,314,600 foot-pounds. 

The duty of a power-pump, expressed in the same manner, 



* A British thermal unit, symbol B. T. U., is the heat absorbed in raising 
one pound of water one degree Fahr. in temperature. 



§255-] H YDRA ULIC MA CHINER Y. 3 2 9 

k the number of foot-pounds of water raised by 751,314,600 
foot-pounds of energy expended on the pump and accessories. 

A committee appointed by the American Society of Me* 
chanical Engineers (see Vol. XL of Transactions American 
Society Mechanical Engineers, p. 668) recommend that in a 
standard method of conducting duty trials, 1,000,000 thermal 
units, or 778,000,000 foot-pounds, be taken as the basis from 
which the duty is computed. This is equivalent to the evapo- 
ration of 10.35 pounds of water per pound of coal, from and 
at 212 , and is likely to be adopted in future trials, in which 
case the duty becomes the number of foot-pounds of water 
delivered for 1,000,000 British thermal units of energy supplied 
the plant. 

The capacity of a pump is usually expressed as the number 
of gallons of water that can be raised against a specified head 
in 24 hours of time; a gallon being considered as equivalent to 
8.3389 pounds at a temperature of 39. 2°. 

255. Measurement of Useful Work. — The useful work 
done by a pump is the product of the number of pounds of 
water delivered into the head through which it is raised. 

The head is the total vertical distance in feet from the sur- 
face of the water-supply to the discharge, increased by friction. 
It is measured most accurately by pressure-gauge connected to 
a Pitot's tube (p. 292) with its nozzle facing the current inserted 
in the discharge pipe, near the pump, and by a vacuum gauge 
or manometer connected to the suction pipe. The head in 
feet is equal to the distance between these gauges plus the 
total readings of the gauges, reduced to equivalent heads of 
water (see p. 324). 

The water delivered may be measured by discharging over 
a weir, or through a nozzle or tapering pipe called a Venturi 
tube. (See Article 204, p. 275.) 

The discharge through a Venturi tube may be taken as 98 
per cent of the theoretical discharge, that through a straight 
conical nozzle as 97.7 per cent.* 

* See papers before Am. Soc. Civil Engineers, by Clemens Herschel, Not, 
1887 and Jan. 1888, and by J, R. Freeman, Nov. 1889. 



33° EXPERIMENTAL ENGINEERING. [§ 25^. 

Delivery measured from Piston-displacement. — Slip. — The 
water delivered in the case of piston-pumps is often computed 
by multiplying the total piston-displacement during the test 
by I, minus the slip. The total piston-displacement is equal to 
the product of area of piston by length of strokes, by total 
number of single strokes. In piston-pumps the length of 
stroke is often variable, in which case especial means must be 
adopted to find the average length. The slip is the percentage 
that the actual delivery is less than the total piston-displace- 
ment ; it can only be determined accurately by comparing the 
volume actually discharged with the total displacement. The 
slip is caused by air in suction-pipe, leakage past piston, leak- 
age past valves in either suction- or discharge-pipe, and imper- 
fect port-openings. The principal cause probably comes from 
leakage past the piston, and this leakage can often be deter- 
mined by removing the cylinder-head, blocking the piston, 
subjecting it to the water-pressure for at least one hour, and 
measuring all the water that leaks past it. This test should be 
repeated for various positions in the stroke. The valve leakage 
can often be determined by a similar test. No air should be 
admitted to the suction-pipe. 

A table of percentage of slip is given in Hill's Manual, 
published by the Harris-Corliss Engine Co., from which it is 
seen that the slip for large pumps is about two per cent, and 
that it varies from one to five per cent. 

256. Efficiency-tests of Pumps. — An -efficiency-test will 
require in each case measurements of, firstly, the energy 01 
work supplied the pump ; secondly, the useful work ; thirdly 
the lost work. 

The difference in methods of testing the various classes of 
pumps, as described in Article 253, simply extends to the meas- 
urement of the power supplied the pump. 

The steam-pump, or steam pumping-engine, is to be con 
sidered as a combination of the steam-engine with a pump. 
The power received by the pump is that delivered by the 
engine, and is determined by a steam-engine test. The 
method of testing steam pumping-engines, and standard method 



§257] H YDRA UL1 C MA CHTNER Y. 3 3 I 

of making duty-trials, as adopted by the American Society of 
Mechanical Engineers, will be given under special applications 
of the method of testing engines. 

The power-pump receives its energy from machinery in 
operation ; the energy received may be measured by a stand- 
ardized transmitting-dynamometer (see Chapter VII.), or, in 
the case of a rotary or centrifugal pump, by mounting in a 
frame having a free angular motion, which is unaffected by the 
tension on the driving-belt. The resistance to rotation is ob- 
tained by a known weight on a known arm, and the power 
supplied in foot-pounds is the product of the circumference 
that might be described by the arm as radius, number of 
revolutions, and the weight. Such a framework is termed a 
cradle-dy namometer. 

257. Special Efficiency-tests— Power-pumps. — Efficiency- 
test of Centrifugal Pumps — Directions. 

Apparatus needed. — Pressure-gauge for delivery, manometer 
for suction, transmission-dynamometer, thermometer, weir for 
discharge. 

Directions. — Connect suction-pipe to supply-tank, and ar- 
range discharge with throttle-valve to deliver water over a 
weir. Connect delivery-gauge to an elongated air-chamber, 
which in turn is connected with the delivery-pipe, provided 
with a water gauge-glass opposite the pressure-gauge, and 
means of changing water-level and air-level.* Connect manom- 
eter or vacuum-gauge to suction-pipe ; obtain vertical distance 
between these gauges. Arrange a standardized transmission- 
dynamometer to receive the power, and drive the pump. 

During the test maintain the water in the air-chamber at 
height of centre of the gauge. 

Testing. — Set the machinery in operation ; arrange the 
throttie-vaive to give an approximate head of 50 feet. After 
uniform conditions are assumed, start the run ; take readings 
once in five minutes of hook-gauge at weir, of temperature of 
water, of discharge-gauge, of sucticn-guage, of dynamometer- 

*See Test of Steam Pumpingengines. 



332 



EXPERIMENTAL ENGINEERING. 



[§2 5 8. 



or power-scale. Continue the run for one hour with uniform 
pressure on discharge-gauge. 

Make a second run with an approximate head of 75 feet, 
and a third run with an approximate head of 100 feet. 

Report. — In report, calculate efficiency, duty, and capacity 
for each head ; draw a curve of each test, using power in foot- 
pounds as ordinates, and total water delivered as abscissae. 
Describe the pump and method of testing. 

Efficiency-test — Rotary Pump — Directions. — Apparatus and 
connections as for centrifugal pump, the power transmitted 
being measured either by a transmission-dynamometer, or by 
a balanced cradle-dynamometer ; the water may be measured 
by a weir, or it may be delivered into two weighing tanks, one 
of which is filling, the other emptying, and the water weighed. 
Directions for the test are as in the preceding. 

258. Form for Log and Report of Pump-tests. — The 
following form for data and report is used at the Massachusetts 
Institute of Technology for log and data of test on Webber 
centrifugal pump and on rotary power-pump : 



No. 



TEST ON WEBBER CENTRIFUGAL PUMP. 

Date 





v 

a 


Water. 


Heads. 


Emerson Power-scale. 




•a 

V 

Pi 

V 

be 

3 
rt 
bo 

ii 

X 


c 


v . 

<~ c 
— 

£S 

p 


<u 

3 

as 
H 


to 

c 

V . 

bet* 

3 £ 

a 3 
be£ 

SB 
|o 


v . 
rt . 

beer 

1 CO 

bc£ 

5" 


c 

c 




3 

13 -J 

< 


c 

U 
1* 


Pumping. 


Tare. 


be 

c 





d 


be 

•5 

u 

<u 
H 


(A 


£ 3 

C C 

si 

Is 


bo 

c 

•3 

!_ 

ii 



a 
3 a 

O u 

> s 

qj — 




























Total . . 


























Av 















































































Diameter discharge-pipe ins. 

Transverse area discharge-pipe , sq. ft. 

Distance between gauges. ■. ft 



§ 258.] 



HYDRA ULIC MA CHINE R V. 



333 



Crest of weif above bottom of channel f: 

Width of weir ft. 

Revolutions of pump per minute 

Water pumped in lbs. 

Duration of test mins. 

o ( Depth of water on weir. , ft. 

> ( Temperature at weir (corrected) ° C ° F. 

' Suction-gauge (corrected) ins. ft. 

Discharge-gauge (corrected) lbs ft. 

Actual suction ft. 

Actual head ft. 

Scale-reading .-.„ » lbs. 

Revolutions per minute 

v ( Scale-reading lbs. 

{2 ( Revolutions per minute 

Water pumped in minutes lbs. 

Capacity in gallons per minute 

Total work by power-scale (pumping) H. P. 

Tare H. P. 

Work given to pump » H. P. 

Work delivered by pump H. P. 

Efficiency per cent. 

Duty (ft. -lbs. per 1,000,000 B. T. U.) 

Signed. , 



•2 ( 



No. 



LOG OF TEST ON ROTARY PUMP. 

Date 





Time. 


Power-scale. 


Gauges. 


Orifices. 


No. of 
Gong. 


Pumping. 


Tare. 


Suction, 

inches 

mercury 


Deliv- 
ery, lbs. 

per 
sq. in. 


Head, 
in feet. 


Temper- 
ature. 




Counter 


Revolu- 
tions. 


Weight. 


C. 


R. 


W. 


















































Av 
























Cor . 

















































334 EXPERIMENTAL ENGINEERING. L§ 2 5 8 

RESULTS OF TEST ON ROTARY PUMP. 

No Date 

Duration of test , min. 

Power-scale, pumping, revolutions per minute 

" weight ... „ . .lbs. 

" tare, revolutions per minute c , t , 

" " weight c lbs. 

Suction-head by gauge inches mercury. ft. H 2 

Discharge-head by gauge lbs. per sq. in " 

Head on orifices " 

Temperature ° C. * F. 

Revolutions of pump per minute 

Area of discharge at gauge sq. ft. 

Vertical distance between gauges ft. 

Diameter of orifices, a.. . ., b. . . ., c. . .., d e. ...,/...., g. . . ., h...., i. . . . 

Coefficients, a. . . ., o...., c. . . ., d. . . ., e. ...,/...., g. . . ., h...., i. . . . 

Constant for power-scale ft. 

Power-pumping, by scale H . P. 

Tare , ,....H. P. 

Power given to pump H. P. 

Velocity-head of discharge ft. 

Total head = press, heads -f- vel. head + vert. dist. bet. gauges ft. 

Water pumped lbs. per sec. 

Work done by pump H. P 

Efficiency of pump per cent. 

Capacity of pump in gallons per minute 

Duty of pump (ft. -lbs. per 1,000,000 B. T. U.) 



Signed. 



Part II. 

METHODS OF TESTING THE STEAM-ENGINE. 



CHAPTER X. 

DEFINITIONS OF THERMODYNAMIC TERMS. 

259. General Remarks. — The methods of testing the 
steam-engine which are given here presume an accurate 
knowledge of the principles of action of the engine, an ac- 
quaintance with the details of its mechanism, and a knowledge 
of the thermodynamic principles which relate to the transfor- 
mation of heat-energy into work. In connection with the 
methods of testing, the student is advised to read one or more 
of the following books : 

Manual of the Steam-engine, by R. H. Thurston. 2 vols. 

N. Y., J. Wiley & Sons. 
Manual of Steam-boilers. Ibid. 
Engine and Boiler Trials. Ibid. 
Etude Experimental Calorimetrique de la Machine a Vapeur, 

par V. Dwelshauvers-Dery. Paris, Gauthier-Villars et Fils, 
Steam-engine, by D. K. Clark. 2 vols. N. Y., Blackie & Co. 
Steam-engine, by C. V. Holmes. 1 vol. London, Longmans, 

Green & Co. 
Steam-engine, by J. M. Rankine. 1 vol. London, Chas, 

Griffin & Co. 
Steam-making, by C. A. Smith. 1 vol. Chicago, American. 

Engineer. 
Steam-using. Ibid. 

335 



;36 



EXPERIMENTAL ENGINEERING. 



[§ 26o. 



Steam-engine, by James H. Cotterill. London, E. & F. N. Spon. 
Thermodynamics, by C. H. Peabody. N. Y., J.Wiley & Sons. 
Thermodynamics, by De Volson Wood. N. Y., J. Wiley & 

Sons. 
Thermodynamics, by R. Clausius. N. Y., Macmillan. 
Steam-tables, by C. H. Peabody. N. Y., J. Wiley & Sons. 
Handy Tables, by R. H. Thurston. N. Y., J. Wiley & Sons. 

260. Relations of Units of Pressure. — The term pressure, 
as employed in engineering, refers to the force tending to com- 
press a body, and is expressed as follows : (1) In pounds per 
square inch ; (2) In pounds per square foot ; (3) In inches of 
mercury ; (4) In feet or inches of water. 

The value of these different units of pressure are as follows: 



TABLE SHOWING RELATION BETWEEN PRESSURE EXPRESSED 

IN POUNDS, AND THAT EXPRESSED IN INCHES OF 

MERCURY, OR FEET OF WATER. 









70 Fah. 




Pressure in 


Pressure in 
pounds per sq. 








pounds per sq. 
inch. 








foot. 


Inches of mer- 
cury. 


Feet of water. 


Inches of water. 


I 


144 


2.0378 


2.307 


27.68 


2 


288 


4.0756 


4.614 


55.36 


3 


432 


6.II34 


6.921 


83.04 


4 


576 


8.0512 


9.23 


IIO.72 


5 


720 


IO.1890 


it. 54 


138.40 


6 


864 


12.2268 


13.85 


166.08 


7 


IOO8 


14.2646 


16.15 


103.76 


8 


1152 


16.3024 


18.46 


221.44 


9 


1296 


18.3402 


20.76 


249.12 


10 


1440 


20.3781 


23.07 


276.80 



The barometer pressure is that of the atmosphere in inches 
of mercury reckoned from a vacuum. At the sea-level, latitude 
of Paris, the normal reading of the barometer is 29.92 inches, 
corresponding to a pressure of 14.7 pounds per square inch. 

Gauge or Manometer pressure is reckoned from the atmos- 
pheric pressure. 

Absolute pressure is measured from a vacuum, and is equal 
to the sum of gauge-pressure and barometer readings expressed 



§ 26 1.] DEFINITIONS OF THERMODYNAMIC TERMS. 337 

in the same units. Absolute pressure is always meant unless 
otherwise specified. 

Pressure below the atmosphere is usually reckoned in inches 
of mercury from the atmospheric pressure, so that 29.92 inches 
would correspond to a perfect vacuum at sea-level, latitude 49 . 

261. Heat and Temperature. — The term heat is used 
sometimes as referring to a familiar sensation, and again as 
applying to a certain form of energy which is capable of pro- 
ducing the sensation. In this treatise it is used in the latter 
sense only. 

Temperature is essentially different from heat, and is merely 
one of its qualities ; it is difficult to define, but two bodies are 
of equal temperature when there is no tendency to the trans- 
fer of heat from one to the other. Temperature is measured 
by the expansion of some substance in an instrument termed 
a thermometer. Two points, that of melting ice and of steam 
from water boiling at atmospheric pressure, are fixed tempera- 
tures on all scales of thermometry. The expansion between 
these points is divided into various parts according to the 
scale adopted, and each part is termed a degree. 

The following thermometric scales are in use in different 
portions of the world : 



Fixed Points, Temperature of Water. 


Fahrenheit. 


Centigrade. 


Rdaumur. 


Degrees between freezing and boil- \ 


180 

32 
I 

1 
4 
"5" 


IOO 
O 

t 

I 

1 


80 


Temperature at freezing point 

Comparative length 1 degree 

< < << << 
t( it << 


O 

t 
f 

I 



Degrees of temperature taken on one scale can easily be 
reduced to any other; thus, let t f be the temperature of a body 
on the Fahrenheit scale, t c on the Centigrade scale, and t r on 
the Reamur scale. We shall have, from the preceding table, 



*/-=K + 32°; 
t. = W f -32 ); 



338 



EXPERIMEN TA L ENGINEERING. 



[§ 262. 



The Fahrenheit thermometer is used principally by English- 
speaking people, and unless otherwise mentioned is the one 
us^d in this treatise. 

The Thermometric Substances principally used are mercury,, 
alcohol, and air, from the expansion of which the temperature 
is obtained. 

Absolute Zero. — This quantity is fixed by reasoning as the 
point where gaseous elasticity or expansion would be zero. 
This is 492 , more exactly 491. 8°, of the Fahrenheit scale or 
2 73° +* °f tne Centigrade scale below the freezing-point of 
water, so that in the Fahrenheit scale the absolute tempera- 
ture is 460 + the reading of the thermometer, and on the 
Centigrade scale 273°-)- the reading of the thermometer. 

Absolute Temperature, on any scale, is temperature reckoned 
from absolute zero. 

262. Specific Heat. — Specific heat is the ratio of that re- 
quired to raise a pound one degree in temperature compared 
with that required to raise one pound of water from 6o° to 61 ° 
Fahr. 

Specific heat of water is not quite constant, but varies as 
follows : f 



Centigrade. 


Fahrenheit. 


Specific Heat. 


Centigrade. 


Fahrenheit. 


Specific Heat. 


o° 


32° 


I.0072 


30° 


. 86° 


O.9954 


5° 


41° 


I . 0044 


35 °o 


95° 


O.9982 


io° 


50° 


I. OO16 


40 


104° 


I . OOOO 


15° 


59° 


I . 0000 


45° 


113° 


I.008 


20° 


68° 


O.9984 


155° 


• 3"° 


I.046 


25° 


77° 


O.9948 


200° 


39 2 ° 


I.046 



Specific heat of saturated steam at atmospheric pressure 
was found by Regnault to equal 0.478. Investigations made 
at Sibley College show that the specific heat of superheated 
steam increases with the pressure and temperature. 

The heat contained in different bodies of the same tempera- 



* Encyc Brit., Vol. XI. p. 573. 



f See Peabody's Steam-tables. 



§ 264.] DEFINITIONS OF THERMODYNAMIC TERMS. 339 

ture, or in the same body in its liquid and gaseous condition, is 
quite different and cannot be measured by the thermometer. 
Thus in equal weights of water and iron at the same tempera- 
ture, the heat in the water is several times that in the iron. 
This is known because in cooling a degree in temperature, 
water will heat a much greater weight of some other substance. 

263. Mechanical Equivalent of Heat. — The experiments 
made by Rumford and Joule established the fact that heat- 
energy could be transformed into work, or vice versa. The re- 
sults of Joule's latest determination gave the mechanical work 
equivalent to the heating of one pound of water one degree Fahr. 
in temperature as 774 foot-pounds, while the later and more 
refined determinations of Rowland, reduced to 45 of latitude 
and to the sea-level, make the mechanical work equivalent to 
the raising the temperature of one pound of water from 62 to 
63 Fahr. to be 778 foot-pounds. The heating of one pound 
of water one degree, from 39 to 40 Fahr., is termed a 
British thermal unit, B. T. U., and this is equivalent in me- 
chanical work to 778 foot-pounds. This number is represented 
by J and its reciprocal by A throughout this work. 

The heat needed for raising one kilogram of water one de- 
gree Centigrade is termed a calorie, and this is equivalent to 
426.9 foot-pounds. 

In some treatises a British thermal unit is the heat required 
to raise one pound of water from 62 to 63 Fahr., which differs 
little from that defined above. 

264. Relations of Pressure and Temperature of Steam, 
— There is a definite relation between the temperature and 
pressure of steam in its normal or saturated condition. This 
relation was very carefully investigated 1836-42 by M. V. Reg- 
nault in Paris by a series of careful experiments made on a large 
scale. These experiments form the basis of our experimental 
knowledge of the properties of steam. 

The properties of steam are also shown by the thermody- 
namic laws, and are given in tables of Rankine, Clausius, M. V. 
Dwelshauvers-Dery, Peabody, and Buel. 

The following empirical formula, deduced from Regnault's 



34° EXPERIMENTAL ENGINEERING. [§ 265. 

experiments, gives the relation between the temperature and 
pressure of steam at a latitude of 45 : 

For steam* from 32 to 21 2° Fahr. pressure in pounds per 
square inch, 

\og/> = a-ba T +cB T , 

in which a = 3.025908, log b = 0.61 174, log c = 8.13204 — 10, 
log a = 9.998181015 — 10, log B = 0.0038134, T=t — 32 . 
For steam from 212 to 428 Fahr., 

lo g p = a 1 -b 1 a 1 T + c 1 B/ t 

in which a x = 3.743976, log b x — 04120021, log c 1 = 7.74168 — 
10, log ^=9.998561831 — 10, \ogB 1 — 0.0042454, T= t — 212 . 
265. Properties of Steam. — Definitions. — Steam occurs in 
two different conditions: 1, saturated ; 2, superheated. 

1. Dry and Saturated Steam, or, as frequently called, dry 
steam, is the vapor of water at point of precipitation, and may- 
be considered the normal condition of steam. 

Saturated steam of any pressure is at the lowest tempera- 
ture and possesses the least specific volume and the greatest 
density consistent with that pressure. The slightest decrease 
in total heat results in partial condensation, forming what is 
termed moist or wet steam, in distinction from dry steam. Thus 
saturated steam may be either wet or dry. The percentage of 
dry steam in a mass of wet steam is termed its quality. 

2. Superheated steam has properties similar in every respect 
to those of a perfect gas. Its temperature is higher, its 
specific volume greater and its density less than saturated 
steam of the same pressure. 

Steam-tables give the properties of dry saturated steam only 
and usually arranged with absolute pressure as the argument 
or given quantity. The important properties are as follows : 

(a) Total Heat (symbol, A). — This is the amount of heat 
required to convert one pound of water from 32 into saturated 

* Steam-tables, by Prof. Cecil H. Peabody. 



§265.] DEFINITIONS OF THERMODYNAMIC TERMS. 34 1 

steam at a pressure P. If t is the temperature of the steam, 
the total heat, A, is calculated by an empirical formula based on 
the experiments of Regnault. Expressed in English units, 

X = 1081.4 + 0.305*. 

(b) Heat of the Liquid (q) is the number of thermal units 
used in heating one pound of water from 32 Fahr. to the tem- 
perature required to generate steam. According to Regnault, 

q == t -f- 0.00002 f -f- o. 0000003 *' 

for Centigrade units. And according to Rankine for English 
units when t x is the initial and t the final temperature, 

q — t — t x + 0.000000103 [(* - 39 - 1 ) 3 — (A — 39°-i) 3 ]- 

(c) Internal Latent Heat (p). — This is the work done, 
measured in thermal units, in separating the molecules of the 
steam beyond the range of mutual attraction. It is calculated 
from the formula 

p = 1061 — 0.791/. 

(d) External Latent Heat (APu). — This is the work, ex- 
pressed in heat-units, of expanding the steam against an 
external pressure which is equal to that of the steam generated. 
Thus, let u = s — <t be the difference in volume of a pound of 
steam, s, and a pound of water, <x, at any pressure per square 
foot, P. Then the work of expansion will be Pu foot-pounds or 
APu thermal units. According to Zeuner, 

APu = 20.91 + i.096(/ — q). 

(e) Heat of the Steam (Z). — This is the heat which the steam 
actually contains; it is the total heat less the external latent 
heat. In thermal units, 

L = X — APu = q -\- p, since X = q -(- APu -\- p. 



34 2 EXPERIMENTAL ENGINEERING. [§266. 

(/) Heat of Vaporization, or total latent heat, (r,) is that por- 
tion of the total heat which is required to convert one pound 
of water at any temperature into saturated steam at the same 
temperature and at a pressure P\ it is the sum of external 
and internal latent heats, or the total heat less the heat of the 
liquid. That is, 

r = p -f- APu = A. — q. 

A formula for calculating r is 

r = 108 1. 4 + 0.305/ — q. 

{g) Specific Volumes and Density of Steam. — These quanti- 
ties are usually calculated from thermodynamic equations. 



dt 



s *= volume of one pound of steam, a = volume of one pound 
of water. 

It will be noticed that the different steam tables differ 
principally in respect to these quantities. 

THERMODYNAMIC CONDITIONS, TEMPERATURE AND 
ENTROPY. 

266. Isothermal is a term used to denote a condition in 
which the temperature remains constant ; the total amount of 
heat, or the pressure, may vary. 

Adiabatic is a term used to denote the condition in which 
the total quantity of heat is unchanged by -heat-transfer. It 
may, however, be changed by transformation into work and 
vice versa. 

Temperature is the scale used to determine the relative 
values of different isothermal conditions ; and change of tern 






§ 266.] DEFINITIONS OF THERMODYNAMIC TERMS. 343 

perature is the change which occurs in passing from one 
isothermal condition to another. 

Entropy is the scale used to determine the relative values 
of different adiabatic conditions ; and change of entropy is the 
change which occurs in passing from one adiabatic condition 
to another. 

Change of temperature can be measured by the expansion 
of some thermometric substance ; but change of entropy, which 
is just as real, cannot be measured or represented in any sim- 
ple manner. If we represent the entropy by 0, the absolute 
temperature by T, the heat at any adiabatic condition by Q, 
then by the second law of thermodynamics 

^ = f (i) 

In case of a liquid, dQ = cdq, in which c is the specific heat, 
and q the temperature. In this case denote the entropy by 6. 
Then 



ycdq 



(2) 



For water this is readily calculated. 

In the case of steam the entropy, or change of entropy 
from water at the freezing-point to steam at any pressure is 
equal to the entropy of the liquid, 0, plus that of the steam, 

-^. In which x is the quality of the steam, or per cent of dry 

steam. 

In this case 



1 



In any other case 



rh- xr J.0- xr 4- I cdt 
<P- T + e -T + I ~T- 



1 i 



344 EXPERIMENTAL ENGINEERING. [§267, 

Change of entropy, 

A short table giving the value of the entropy of the liquid 
is to be found in Article 230, page 301. 

267. Steam-tables. — The numerical values representing 
the various properties of steam, in relation to its pressure, are 
arranged in the form of tables termed steam-tables. The rela- 
tive accuracy of these various steam tables is discussed at 
length by Prof. D. S. Jacobus in Vol. XII. Transactions of 
American Society Mechanical Engineers, page 590, from which 
it is seen that the table compiled by Mr. Chas. T. Porter rep- 
resents the experimental investigations of Regnault most accu- 
rately ; but that possibly for scientific investigations the tables 
of Peabody, Dery, and Buel, which are founded on thermo- 
dynamical laws, are somewhat more accurate. Practically the 
tables are accordant for all working pressures and temperatures 
of steam ; the difference is principally in the values given for 
the density. The tables of Chas. T. Porter* have been adopted 
as the tables to be used in reporting results of boiler trials 
and of duty trials of pumping engines, by the American 
Society of Mechanical Engineers (see Transactions, Vol. VI., 
and also Vol. XII.), and for such tests the standard reports 
should be calculated from those tables. These tables are, how- 
ever, deficient for scientific purposes, since they omit values of 
some of the important properties of steam. In the Appendix 
is printed the table by Porter, and also the table by Buel as 
printed in Weisbach's work on the steam-engine and in Vol. I. 
of Thurston's Manual of the Steam-engine. 

* The Richards Steam-engire Indicator, by Chas. T. Porter. 



CHAPTER XL 



MEASUREMENT OF PRESSURE. 



268. Manometers. — The term manometer is frequently 
applied to any apparatus for the measurement of pressure : 
although it is the practice of Ameri- 
can engineers to use this term only for 
short columns filled with mercury or 
water and used to measure small press- 
ures. The pressure is measured, in all 
manometers used for engineering pur- 
poses, above the atmospheric pressure, and 
this determination must be increased by 
the pressure equivalent to the barometer- 
reading to give absolute pressure. The 
manometers in common use are glass or 
metal tubes, either U-shape in form as in 
Fig. 160, or straight and connected to a 
cistern of large cross-section as shown in 
Fig. 162. 

Pressures below the atmosphere can 
be measured equally well by connecting 
to the long branch of the tube and leav- 
ing the short branch open to the atmos- 
phere. 

269. U-shaped Manometer. — In the 

U-shaped tube, with any form as shown in Fig. 160 or Fig. 161, 

345 




Fig. 160.— (/-shaped Ma- 
nometer-tubes. 



346 



EXPERIMEN TA L ENGINEERING. 



[§ 269. 



water or mercury is poured in both branches of the tube, the 
pressure is applied to the top of one of the tubes, 
and the liquid rises a corresponding distance in the 
other. When no pressure is applied, the liquid will 
stand at the same level in both tubes ; when pressure 
is applied, it is depressed in one tube and raised in 
the other. The pressure corresponds to the vertical 
distance between the surface of the liquid in the 
two tubes and can be reduced, as explained in Arti- 
cle 260, to pounds of pressure per square inch. 

An inch of water at a temperature of jo° Fahr. 
corresponds to a pressure of 0.036 pound ; an inch 
of mercury, to 0.493 pound. The principle of ac- 
tion of the U-shaped manometer-tubes is as follows : 
Consider the atmospheric pressure as acting on 
one side of the tube, and the pressure which is 
to be measured and which is greater or less than 
atmospheric as acting on the other side. The total 
absolute pressure in each branch of the tube must be 
equal, consequently enough liquid will flow from the side of. the 
greater to the side of the less to maintain equilibrium. Thus 
let p be the atmospheric pressure ; p x , the absolute pressure 
to be measured, expressed in inches of water or mercury ; k, 
the height of the column on the side of the atmosphere; h x> 
the height on the side of the pressure. Then 



Fig. 161. 
U-shaped Ma 

NOMETER. 



from which 



f + *=A + *i> 



Pi-P = h-K 



The U-shaped tube, in construction similar to Hoadleys 
draught- gauge, Art. 275, can be used with two liquids of dif- 
ferent densities, using the heavier liquid on the side of the 
lighter pressure. Let d x denote the density of the lighter 
liquid, and d that of the heavier; h v and //, the corresponding 



§ 27O.J MEASUREMENT OF PRESSURE. 2)47 

heights of the columns. We shall have as before, taking all 
measurements from the lower surface of the heavier liquid, 



p l + fid = p + k 1 d 1 , 
from which 

p x — p = h x d x — hd. 

This instrument is much more delicate and is better suited 
for measuring small differences of pressure than when a single 
liquid is used ; the reason for which will be readily seen if we 
consider an example. Suppose that water be used as the 
heavier liquid, of which the specific gravity is I, and that 
crude olive-oil be used as the lighter liquid, of which the 
specific gravity is 0.916. Suppose that all pressures are meas- 
ured in equivalent height of a water column expressed in 
inches, and that h = 6 inches,/, — p = \ inch ; then h x , which 
is the difference of level of the water in the two branches, will 
be \ -f- 6.(0.916) = 6.0 inches, whereas it would have been but 
one-half inch had there been only water, or 0.545 if the liquid 
had been olive-oil. By making the density of the liquids more 
and more nearly equal the instrument will become more and 
more delicate. A dilute mixture of water and alcohol of which 
the density must be determined (see Article 275, page 354), for 
the heavier, and of crude olive-oil for the lighter, gives excel- 
lent results. If the instrument can be so manipulated that 

p^-p=_h(d x -d\ 

and the calculation becomes very simple, as in that case the 
reading would have to be multiplied only by the differences oi 
the densities of the two liquids. 

270. Cistern-manometer.— In the case of a manometer oi 
the form of Fig. 162 or Fig. 163, the cistern or vessel into 



348 



EXPERIMENTAL ENGINEERING. 



[§ 270. 



which the tube is connected has a large 
that of the tube. Pressure is applied to 
the top of the liquid in the cistern, the 
surface of which will be depressed a small 
amount, and the liquid in the tube will 
be raised an amount sufficient to balance 
this pressure. The pressure corresponds 
to the vertical distance from the surface 
of the liquid in the tube to that in the 
cistern. As the liquid is not usually in 
sight in the cistern, a correction is neces- 
sary to the readings in order to find the 
correct height corresponding to a given 
pressure. This correction is calculated 
as follows : Let A equal the area of sur- 
face of the liquid in the cistern, a the 
area of the manometer-tube, H the fall 
of liquid in the cistern, h the correspond- 
ing rise of liquid in the tube, b the height 
required for one pound of pressure (see 
Article 260, page 336), p the number of 
pounds of pressure. We have then 



area relative to 



H 



P\ 







162. — Cistern-manom- 
eter. 



and since the tube is supplied by liquid from the cistern, 

HA = ha. 



Eliminating H in the two equations, 

Apb 



If p = one pound, 



h = 



k = 



A+a 

Ab 
A+a' 



§ 2 7 2.] 



MEASUREMENT OF PRESSURE. 



349 



which is the length the graduation should 
be made to allow for fall of mercury in the 
cistern and give a value equal to one pound 
of pressure. 

To make this correction uniformly ap- 
plicable the area of cross-section of both 
tube and cistern should remain uniform. 

271. Mercury Columns. — Mercury col- 
umns, as used in the laboratories, are usually 
made on the principle of the cistern-manom- 
eter. The tube is very long and made of 
glass or steel carefully bored out to a uniform 
diameter. If the tube is of glass, the height 
of mercury can be readily perceived and 
read ; if of steel, the height of the mercury 
is usually obtained by a float, which in some 
instances is connected to a needle which 
moves around a graduated dial. 

In some of these instruments electric con- 
nections are broken whenever the mercury 
passes a certain point, and an automatic 
register of the reading is made. Fig. 163 
shows the usual form of the mercury col- 
umn, in which the pressure is applied in the 
upper part of the cistern, so as to come 
directly on the top of the mercury. In the 
case of a glass column the graduations are 
usually made on an attached scale, and are 
corrected as explained in Article 270 for the 
fall of mercury in the cistern. 

272. Corrections to the Mercury Col- 
umn. — The mercury column is usually the 
standard by which all pressure-gauges are 
compared, and its accuracy should be 
thoroughly established in every particular. 

The requirements for an accurate mer- 
cury column are : 



I IOO- 

F 

I 90 



as 



fh 



ii ;..:i 



m 



Fig. 



163. — Mercury 
Column. 



350 



EXPERIMENTAL ENGINEERING. 



L§ 272. 



1. Uniform bore in cistern and tube. 

2. Accurate graduations, spaced as explained in Article 270. 
As it is impossible to make the graduations perfectly accurate, 
the error in this scale should be carefully determined, and the 
readings corrected accordingly. 

The corrections to the readings are: 

1. For expansion of the mercury and tube due to increase 
of temperature. 

The method of correcting for expansion of the mercury and 
the material enclosing it would be as follows : 

Let A equal the coefficient of lineal expansion of the mer- 
cury, and 3A. that of the cubical expansion per degree Fahr. ; 
let S equal the coefficient of lineal expansion of the metal of 
the cistern, and S' that of the metal of the tube. Let H' equal 
the depression in the cistern, h' the corresponding elevation in 
the tube corresponding to a pressure of one pound, and a 
difference of level of b ' . Let b equal the difference of level 
corresponding to a pressure of one pound at a temperature of 
6o° Fahr. Then, as before, 



ti 



A'V 



a' +~A' 



A(i+2S)b(i+ 3 \) 
a(i +2d') + A(i +2$)' 



2. Correction for the capillary action of the tube. This force 
depresses the mercury in the tube a distance which decreases 
rapidly as the diameter increases. 

The amount of this depression is given in Loomis's Meteor- 
ology as follows : 



Diameter of 
Tube. 
Inch. 


Depression. 
Inch. 


Diameter of 
Tube. 
Inch. 


Depression. 
Inch. 


O.05 
O. IO 
O.I5 
0.20 
O.25 
O.30 
0-35 


O.295 
0. 141 
O.087 
O.058 
O.041 
O.029 
0.02I 


O.40 

0.45 
O.50 
O.60 
O.70 
O.80 


O.OI5 

O.OI2 

0.008 

0.004 

O.OO23 

0.0012 



§^73-] MEASUREMENT OF PRESSURE. 35 I 

3. There might also be considered a very slight correction 
due to the fact that the force of gravity in different latitudes 
varies somewhat. Since the weight of a given mass of mercury 
is equal to the product of the mass into the force of gravity, it 
will vary directly as the force of gravity, or, in other words, 
the assumed weight of mercury may not be exactly correct. 
This correction is a refinement not necessary in usual tests. 

4. Difference of barometer-readings at top and bottom of 
the tube might make some difference. 

While it is well to give all these corrections their true 
weight, yet a false impression should not be incurred concerning 
their importance. It is hardly probable that the corrections for 
change in temperature, or corrections for the difference in the 
force of gravity from that at the sea-level on the equator, would 
in any event make a sensible difference in the readings. 

273. Direct-reading Draught-gauges. — The ascending 
force which causes smoke or heated air to rise in a chimney is 
called the draught. The pressure in such a case is below that 
of the atmosphere, and is usually measured in inches of 
water. Draught-gauges are U-shaped manometers adapted to 
measure pressures less than that of the atmosphere. See Figs. 
160 and 161. To use this manometer, water is poured into the 
tube until it stands at the point marked o, Fig. 161; one side 
is then connected by a pipe to the flue or chimney of which 
the draught is to be measured. The difference of level of the 
water, as shown by the manometer-tubes, is the draught ex- 
pressed in inches of water. An inch of water at a temperature 
of 70 Fahr. corresponds to 0.036 pound. 

Allerts Dr aught- gauge. — A very complete draught-gauge of 
the U-shaped manometer type, with attached thermometer and 
a movable scale the zero of which can be set to correspond to 
the lower water surface, is shown in Fig. 164 as designed by 
J. M. Allen of the Hartford Boiler Insurance Co. 

A draught-gauge designed by the author is shown in Fig. 
164a, which is arranged so that one scale will give difference in 
elevation of the liquid in the two columns. This is accomplished 



352 



EXPERIMENTAL ENGINEERING. 



[§ 274. 



by setting the collar F to the lower meniscus of the liquid by the screw 
E\ then by setting the collar H to the meniscus of the liquid 
in the other column by means of the micrometer- screw R, the 
height of the column may be read on the attached scale and the 





Fig. 164. — Draught-gauge. 



Fig. 164a. — Draught-gauge- 



micrometer- screw R. The reflection from the two edges of the 
meniscus enables the scales to be set with great accuracy. The 
inches and tenths of inches are read on the attached scale, the 
hundredths of inches by the graduations of the micrometer- screw R. 
274. Draught-gauges with Diagonal and Level Scales. 
— Peclel's Draught- gauge. — A draught-gauge with diagonal scale 
is shown in Fig. 165. It consists of a bottle, A, with a mouth- 
piece near the bottom into which a tube, EB, is inserted with any 
convenient inclination. The upper end of the tube is bent up- 
ward, as at BK, and connected with a rubber tube, KC, leading 
to the chimney. The tube is fastened to a convenient support, 



275-] 



MEASUREMENT OF PRESSURE, 



353 



and a level, D y is attached. To use the instrument, first level 
it, note reading of scale, then attach it to the chimney, and 
take the reading, which will be, if the inclination is one to five, 




Fig 165. — Draught-gauge 



A 



SsJ 



Fig 166.— Higgins's Draught- 
gauge. 



five times the difference of level in the bottle and tube. The 
scale should be graduated to show differences of level in the 
bottle, and thus give the pressure directly in inches of water. 

Higgins's Draught-gauge. — Another form of this class of 
draught-gauges is shown in Fig. 166, as designed by Mr. C. P. 
Higgins of Philadelphia. The gauge 
is filled with water above the level of 
the horizontal tube, in such a manner 
as to leave a bubble of air about one- 
half inch long near one end of the hori- 
zontal tube when the water is level in 
the side tubes. The inside diameter 
of the vertical tubes being the same, say one-half inch, and that 
of the horizontal tube one eighth of an inch, a draught equivalent 
to one inch in water, or which will cause the water-level in the 
vertical tubes to vary one inch, will cause the bubble in the 
tube to move eight inches in the horizontal tube. In general 
the air-bubble moves a distance inversely proportional to the 
area of the tubes, and hence it can be read more accurately 
than in case of the ordinary draught-gauge. 

275. Hoadley's Draught-gauge. — This gauge was used in 
the trials of a warm-blast apparatus described in Vol. VI. Tran- 
sactions American Society Mechanical Engineers, page 725. 
It consists of two glass tubes, as shown in Fig. 167, about 30 
inches long, and about 0.4 inch inside diameter and 0.7 inch 
outside, joined at each end by means of stuffing-boxes to 
suitable brass tube connections, by which they are secured to a 



354 



EXPERIMEN TA L ENGINEERING. 



L§ 275. 



backing of wood. The glass tubes can be put in communica- 
tion with each other at top and bottom by opening a cock in 
each of the brass connections. Directly over each tube is a brass 
drum-shaped vessel 4.25 inches in diameter and 
with heads formed of plate-glass. These drums 
are connected to the tubes, and also provided 
with stop-cocks and nipples to which rubber 
tubes can be attached. Two sliding-scales are 
arranged along the tubes, one to measure the de- 
pression, the other the elevation, of the surface of 
a liquid filling the lower halves of the tubes. In 
the use of the instrument two liquids of different 
densities were used, a mixture of water and 
alcohol with specific gravity about 0.93 being 
used for the heavier liquid, and crude olive-oil 
with a specific gravity of 0.916 for the lighter. 
In using the instrument the heavier liquid was 
first put into the tubes, care being exercised to 
avoid wetting the top attachments ; then the 
top connection between the tubes was opened 
and the olive-oil poured in. In using the instru- 
ment one branch was connected to the chimney, 
the other being opened to the air, the bottom 
connection opened and the top connection 
closed. The liquid would rise in the tube with 
the lighter pressure a distance inversely pro- 
portional to the respective areas of exposed 
surface of the tube and drum. The bottom 
connection was then closed, the connection to 
the flue removed, and the top connection opened ; 
the surface of the olive-oil would then become 
level in the two tubes, that of the water remaining at different 
heights. It was then attached to the flue and these operations 
repeated, until the heavier liquid would no longer flow to the 
side of the lighter pressure; in that case we should have the 
condition of equilibrium between two liquids of different den- 
sities, Article 269, page 347, in which the lengths of columns 



Fig. 167. — HoAn- 
ley's Dkaughi- 

GAUGE. 



§ 276.] 



MEASUREMENT OE PRESSURE. 



355 



of the two liquids are equal. Hence, noting that p is here the 
greater, the difference of pressure in inches of water is 

p-p 1 = h(d 1 -d), 
in which d\ and d are the respective specific gravities of the 
liquids used. 

276. Multiplying Draught-gauges. — Fig. i6Sa shows a 
draught-gauge designed by Prof. Wm. Kent, the dimensions of 
which are marked on the figure, although they are not material for 
its operation. The gauge consists of a cup, B, which is partly filled 
with water, and an inverted cup, A, suspended above the cup B 
by a spring, C, with the lower and open end submerged in the 
water of the cup B. The tube, E, extends through the side of 
the cup B, with its upper end projecting above the surface of 
the water in the cup B, and is extended by suitable connection 
to the flue. 





Fig. 168&. 

By this connection the pressure in the inverted cup, A, is re- 
duced to that in the flue where the pressure is to be measured, 
putting a greater load on the spring, C, which causes it to elongate. 
The amount of elongation will be proportional to the reduction 
in pressure and can be determined by the use of a suitable scale, 
the values of which are found by calibration. It is evident that 
the distance through which the cup A will move is dependent 
upon the area of its cross-section and the strength and length 
of the spring, C, and the immersion in the water. 



3$6 EXPERIMENTAL ENGINEERING. [§ 276. 

Peclet in his work, "Traite de la Chaleur," published in 1878, 
describes a similar gauge. 

In Vol. XI of the Transactions of the Am. Soc. Mech. En- 
gineers Prof. J. B. Welb describes a draught-gauge of similar 
principle, but in which the change in pressure is weighed on a 
pair of balances. 

A U-shaped gauge as shown in Fig. i6Sb, in which two liquids 
of different density are employed, has been frequently used to 
measure small pressures. In the gauge shown, each arm of the 
U tube is enlarged near its upper end for a short distance. Sup- 
posing the liquids employed to be water and kerosene oil, water 
is first put into the U tube in one of the arms, as, for instance, 
the arm B; kerosene oil is put in the arm A, the surface of both 
liquids being in the enlarged parts C and D. If the side con- 
taining the lighter liquid is connected to the flue, the surface in 
the enlarged portion B will move in proportion to the pressure. 

If a be the point of junction of the heavier and lighter liquids, 
this motion will be as much greater than the surface D as the 
area is smaller; if, for instance, the area at a be one fourth that 
at D, the motion will be four times as great. The motion of 
the surface A could be determined by calculation, but it can be 
much more accurately and more easily determined by a calibra- 
tion, which consists of a comparison with a direct- reading draught- 
gauge used to measure the same pressure. 

A form of pressure-gauge has been made in which the pres- 
sure has been transmitted to the measuring manometer by a 
piston having faces or sides of unequal areas connected. In 
this case the total pressure acting on each face of the piston 
will be in equilibrium ; consequently the pressure per square inch 
on each face will vary inversely as the areas of the two faces 
of the piston. The objection to the instrument is the resistance 
due to friction of the piston, which can in large measure be elimi- 
nated by keeping it in rotation during its use. In place of a 
piston two diaphragms of unequal area with a connecting solid 
part have in some cases been employed for the purpose of eliminat- 
ing friction. 



§ 277-] 



MEASUREMENT OF PRESSURE. 



357 



277. Steam-gauges. — The steam-gauges in general use are 
of two classes, known respectively as the Bourdon and Dia- 
phragm Gauges. 

The Bourdon Gauge. — In the Bourdon gauge the pressure 
is exerted on the interior of a tube, oval in cross-section, bent 
to fit the interior of a circular case ; the application of pressure 
tends to make the cross-section round and thus to straighten 
the tube. This motion communicated by means of racks and 
gears rotates an arbor carrying a needle or hand. 

The various forms of levers used for transmitting the 
motion of the tube to the needle are well shown in the accom- 




Fig. 169. — Crosby Bourdon Gauge. 



panying figures, 169 to 173. The levers are in general adjust- 
able in length so that the rate of motion of the needle with 
respect to the bent tube can be increased or diminished at will. 
Thus in Fig. 169, and also in Fig. 170, the lever carrying the 
sector is slotted where it is pivoted to the frame ; by loosen- 
ing a set-screw the pivot can be changed in position, thus alter- 
ing the ratio of motion of hand and spring in different parts of 
the dial. 

Fig. 170 shows a gauge with a steel tube or diaphragm for 
use with ammoniacal vapors which attack brass. 



353 



EXPERIMENTAL ENGINEERING. 



[§ *77- 




FlG. 170. — SCHAEFFER & BuDENBERG AMMONIA-GAUGE. 




Fig. 171. — Bourdon Gauge. 



In nearly all these gauges lost motions of the parts are 
to some extent taken up by a light hair-spring wound around 
the needle-pivot. 



§ 2 7 8.] 



MEASUREMENT OF PRESSURE, 



359 



278. The Diaphragm Pressure-gauge. — In the dia- 
phragm-gauge the pressure is resisted by a corrugated plate, 
which may be placed in a horizontal plane, as in Fig. 172, or in a 
vertical plane, as in Fig. 173. The motion given the plate is 
transmitted to the hand in ways similar to those just explained. 




Fig. 172. — Diaphragm-gauge. 



In Fig. 172 the pressure is exerted on the corrugated dia- 
phragm below the gauge, and the motion is transmitted to the 
hand by the rods and gears shown in the engraving. 

The construction shown in Fig. 173, in which the diaphragm 
is vertical, is as follows : the lever is in two parts which are 
pivoted at the centre; one end is fixed to the frame, the other 
connected to the sector. The centre pivot is pressed outward 
by the action of the diaphragm, drawing the free end downward 
and rotating the sector, which in turn moves the needle. 

In gauges of usual construction of either class, when there 
is no pressure on the gauge, the needle rests against a stop, 
which is placed somewhat in advance of the zero-mark, so that 



360 



EXPERIMENTAL ENGINEERING 



[§ 2/9. 



minute pressures are not indicated by the gauge. In the use 
of the instrument the needle sometimes gets k>ose on the pivot, 
or turned to the wrong position with reference to the gradua- 
tions ; in such a case the needle is to be removed entirely, and 
set when the gauge is subjected to a known pressure. These 




Diaphragm-gauge. 



gauges are also affected by heat. Hence, when set up for use a 
bent tube, termed a siphon, or a vessel which will always contain 
water, should be interposed between the gauge and the steam. 
279. Vacuum-gauges. — Vacuum-gauges are constructed 
in the same method as the Bourdon or diaphragm gauges; the 
removal of pressure from the interior of the bent tube or dia- 
phragm causes a motion which is utilized to move the needle. 
These are graduated to show pressure below that of the at- 
mosphere corresponding to inches of mercury, zero being at 
atmospheric pressure, and 29.92 a perfect vacuum. The differ- 
ence between the reading by such a gauge and that of the 



§ 280.J 



MEASUREMENT OF PRESSURE. 



361 



barometer would be the absolute pressure in inches of mer- 
cury. 




Fig. 174.— Edson*s Speed and Pressure Recording Gauge and Alarm. 



The principal makers of steam-gauges in this country are the 
Crosby Steam Gauge and Valve Co., Boston ; American Steam 
Gauge Co., Boston; Ashcroft Steam Gauge Co., New York; 
Schaeffer & Budenberg, New York ; Utica Gauge Co., Utica, 
N.Y. 

280. Recording- gauges. — Recording-gauges are arranged 
so that the pressure moves a pencil parallel to the axis of a 
revolving drum which is moved at a uniform rate by clock- 
work. The Edson recording-gauge is shown in Fig. 174. In 
this gauge the steam-pressure acts on a diaphragm which oper- 



362 



EXPERIMENTAL ENGINEERING. 



[§ 2*50. 



furnished 



ates a series of levers giving motion to a needle moving over 
a graduated arc showing pressure in pounds ; also to a pencil- 
arm moving parallel to the axis of a revolving drum. 

This instrument has an attachment, which is 
when required, to record fluctuations 
in the speed, and consists of a pul- 
ley on a vertical axis below the instru- 
ment that is put in motion by a belt 
to the engine-shaft. On the small 
pulley-shaft are two governor-balls 
which change their vertical position 
with variation in the speed, giving 
a corresponding movement up or 
down to a pencil near the lower part 
of the drum. A diagram is drawn 
on which uniform speed would be 
shown by a straight line. 

Fig. 175 shows Schaeffer & Buden- 
berg's recording-gauge. This con- 
sists of a pressure-gauge below the 
recording mechanism. The drum B 
is operated by clock-work, the piston- 
rod C, which carries the pencil, being 
moved by the pressure. The pencil- 
movement is much like that on the 

t, . . . .... Fig 175* — Recording Pressure- 

Kichards steam-engine indicator. gauge. 

Fig. 176 shows a portion of a diagram made by a recording- 
gauge. The drum is operated by an eight-day clock, and ar- 





Fig. 176.— -Diagram from Pressure-recording Gauge. 



§ 28 1.] MEASUREMENT OF PRESSURE. 363 

ranged to rotate once in twenty-four hours. In the diagram 
the ordinates show pressure, and the abscissae time in hours 
and fractions of an hour. 

281. Apparatus for Testing Gauges. — Apparatus for 
testing gauges consists of a pump or other means of obtaining 
pressure, and some method of attaching the gauge to be tested, 
and the standard with which it is to be compared. The form of 
pump usually employed for producing the pressure is shown in 
Fig. 177. The gauge is attached at £, the standard at E x ; the 
hand-wheel D is run back, and water is supplied by filling the 
cup between the gauges and opening the cock; after the cylin- 
der C is filled the cock below the cup is closed ; if the hand- 
wheel D is turned, an equal pressure will be put on the standard 
and on the gauge. 

The standards used for testing may be manometers or cab- 
brated gauges, or apparatus for lifting known weights by the 
pressure acting on a known area. Of these various standards, 
the mercury column, as described in Article 271, page 349, is 
to be given the preference, since the only errors of any prac- 
tical importance are those due to graduation. The readings 
given by the mercury column are on a larger scale than those 
given by any other instrument, and no corrections for friction 
are required. The other standards, of which the short mer- 
cury columns have been described (see Article 264), will be 
found to give excellent results in practice, since the graduations 
on the gauges to be tested are usually so close together that 
the friction of the moving parts of the apparatus is inap- 
preciable. 

Apparatus for Testing Gauges with Standard Weights, 

There are two forms of this apparatus on the market, in one 
of which the pressure is received on a round piston, and in 
the other on a surface exactly one square inch in area. The 
friction in both cases is practically inappreciable ; the errors in 
areas can be determined by comparison with a standard mer- 
cury column. 

The Crosby Steam-gauge Testing Apparatus. — This is shown 
in Fig. 178, from which it is seen to consist of a small cylinder 



3^4 



EXPERIMENTAL ENGINEERING. 



[§ 23 JU 




Wig. 177.— Test-pump for Gauges. 



§28l.J 



MEASUREMENT OF PRESSURE. 



365 



in which works a nicely fitted piston ; this cylinder connects 
with a U-shaped tube ending in a pipe tapped and fitted for 




Fig. 178.— Crosby Steam-gauge Testing Apparatus. 

attaching a gauge. The tube is filled with glycerine, in 
which case a known weight added to the piston produces an 
equal pressure on the gauge, less the friction of the piston in 
the tube. This is almost entirely overcome by giving the 
weight and piston a slight rotary motion. 

The Square-inch Gauge. — This apparatus consists of a tube 
the end of which has an area of one square inch enclosed with 
sharp edges. This is connected to the test-pumps in place of 
the standard (see Fig. 177, page 364); a given weight is sus- 
pended from the centre of a smooth plate which rests on the 
square inch orifice. The gauge to be tested is connected at 
E, and the pressure applied until the plate is lifted and water 
escapes from the orifice. 



366 EXPERIMENTAL ENGINEERING. [§ 282- 

282. Calibration and Correction of Pressure-gauges. — 

The correctness of gauges is determined in each case by com- 
parison with apparatus known to be correct, the apparatus 
being subject to a fluid pressure of the same intensity. The 
calibration may be done by comparison with any of the stand- 
ards described. 

Calibration of Gauges with the Mercury Column. 

First, with Steam-pressure. — In this case attach the gauge 
with a siphon connection to a steam-drum, making the center 
of the gauge the height of the zero of the column. This drum 
is to be connected at one end to the mercury column, and the 
steam-pressure is to be applied to it so that it can be regulated 
by throttling the admission or discharge. Admit steam- 
pressure to the gauge and the mercury column ; adjust the 
pressure to a given reading by throttling the valves. Starting 
at five pounds of pressure on the gauge, note the correspond- 
ing reading of the mercury column, temperature of the mer- 
cury and of the room. Increase the pressure and take readings 
once in five pounds. In no instance allow the pressure to exceed 
that at the time of making the reading. In case the pressure is 
made too great at any time, run it some distance below the 
required amount and make a new trial, it being necessary to 
keep the mercury column and gauge hand moving continually 
upward or downward. Repeat the same operation in the 
reverse direction, commencing with the highest pressures ; the 
average reading of the mercury column, corrected for error as 
explained in Article 272, page 350, and reduced to pounds of 
pressure, is the correct pressure with which the gauge-reading 
is to be compared. 

Second, with Water-pressure. — In this case a hand force- 
pump (see Article 281) must be used after the limits of pressure 
• of the water-main have been reached. Proceed as follows: 

Run out the piston of the pump attached to the mercury 
-column to the end of its travel ; close drip-cock and open the 
■ connectiag-valve. Attach the gauge to be tested with its 
centre opposite the zero of the column. Open the cock. 



§ 28 3 .] 



MEASUREMENT OF PRESSURE. 



367 



Draw water from the mains until the gauge indicates 5 lbs. 
pressure. Shut off the water and adjust the pressure exactly 
at 5 lbs. by using the displaces Note the height of the mer- 
cury in the tube. Increase the pressure to 10 lbs. and take 
readings. Carry the pressure as far as desired by increments 
of 5 lbs. Use the pump alone when water-pressure fails. 
From the maximum pressure attained descend by increments 
of 5 lbs., taking readings as before. Tabulate data and plot a 
curve, using gauge-readings as ordinates and actual pressures as 
abscissae. By inspection of the curve determine the fault in 
the gauge and give directions for correcting it. 

In these tests it may not be possible to set the centre of 
the gauge as low as the zero of the column. In that case the 
reading on the mercury column should be greater than that at 
the centre of the gauge by a pressure due to the length of a 
column of water equal to the elevation of the' centre of the 
gauge above the zero of the -mercury column. This is a con- 
stant amount ; it should be obtained and the read- 
ings of the column corrected accordingly. 

The method of calibrating gauges with other 
standards is to be essentially the same, except as to 
the manipulation of the apparatus. Further di- 
rections do not seem necessary. 

Correction of Gauges. — If an error appears as a 
result of calibration, it may generally be corrected ; 
if the error is a constant one, the hand may be 
removed with a needle-lifter, and moved an amount 
corresponding to the error, or in some gauges the 
dial may be rotated. If the error is a gradually 
increasing or diminishing one, it can be corrected by 
changing the length of the lever-arm between the 
spring and the gearing by means of adjustable sleeves 
or the equivalent. It is to be noted that the pin 
to stop the motion of the hand is not placed at 
zero, but in high-pressure gauges is usually set at u-shS-eJma- 
three to five pounds pressure. 

283. Calibration of Vacuum-gauges. — This is best done 
by a comparison with a U-shaped mercury manometer, as shown 



368 



EXPERIMENTAL ENGINEERING. 



[§284. 



in Fig. 179, of which each branch of the tube should exceed 
30 inches in length. Before calibrating, the manometer is 
filled with mercury to one half the length of the tubes, and 
is attached near the gauge to be tested to the receiver of an 
air-pump. In case a condensing engine is used, both the 
gauge and the standard may be connected to the condenser. 
A comparison of the readings of the vacuum-gauge with the 
difference of level of mercury in the two tubes will determine 
the error of the gauge. 

284. Forms for Calibration of Gauges. 

CALIBRATION OF STEAM-GAUGE BY COMPARISON WITH THE 

MERCURY COLUMN. 
Maker and No. of Gauge. 



Date. 



189 



Observers, 



No. 



Gauge, 
lbs. 


Mercury Column. 


Gauge, 
lbs. 


Inches. 


Pounds. 


Up. 


Down. 


Mean. 















Error, 
lbs. 



Temperature of Room .... deg. Fahr. 
Centre of Gauge above o of column . . ft. 
Correction to column reading .... lbs. 

CALIBRATION OF STEAM-GAUGE BY COMPARISON WITH THE 
SQUARE-INCH GAUGE, OR WITH CROSBY'S GAUGE- 
TESTING APPARATUS. 



Maker and No. of Gauge 



Date 189 . Observers 



■\ 



No. 



Load in lbs. on 
Valve. 



Gauge. 



Error. 



Remarks. 



CHAPTER XII. 
MEASUREMENT OF TEMPERATURE. 

285. Mercurial Thermometers. — Measurements of tem- 
perature are determined by the expansion of some ther- 
mometric substance, mercury, alcohol, or air being commonly 
employed. 

The mercurial thermometer is commonly used ; this con- 
sists of a bulb of thin glass connected with a capillary glass 
tube ; on the best thermometers the graduations are cut on 
the tube, and an enamelled strip is placed back of them to facil- 
itate the reading. When the mercury is inserted, every trace of 
air must be removed in order to insure perfect working. There 
are certain defects in mercurial thermometers due to perma- 
nent change of volume of the glass bulb, with use and time, 
that results in a change of the zero-point. This defect is so 
serious as to render the mercurial thermometer useless for very 
minute subdivisions of a degree. In a good thermometer the 
bore of the tube must be perfectly uniform, which fact can be 
tested by separating a thread of mercury and sliding it from 
point to point along the tube, and noting by careful measure- 
ment whether the thread is of the same length in all portions 
of the tube : if the readings are the same, the bore is uniform or 
graduated by trial. In most thermometers the graduations are 
made with a dividing engine ; in some thermometers the prin- 
cipal graduations are obtained by the thread of mercury, as 
described ; in the latter case change in diameter of bore would 
be compensated. To determine the accuracy of temperature 

369 



37° EXPERIMENTAL ENGINEERING. [§ 286. 

measurements thermometers used should be frequently tested 
for freezing-point and boiling-point. The accuracy of inter- 
mediate points shouid be determined by comparison with a 
standard mercurial or air thermometer. 

The mercurial-weight thermometer which was employed by 
Regnault, but is now very little used, consists .of a glass vessel 
with a large bulb and capillary tube, open at the top ; it is filled 
with mercury when at the temperature of the freezing-point ; 
it is then heated to the temperature of boiling water, and the 
amount of mercury that runs out is carefully weighed, and de- 
termines the value of the thermometric scale. The temperature 
of any enclosure is then found by placing in it the thermome- 
ter, previously filled when at freezing-point and weighing the 
amount that escapes ; from this the temperature can be cal- 
culated by simple proportion. 

The expansion of mercury is not perfectly uniform for all 
temperatures, so that mercurial thermometers are never per- 
fect for extreme ranges of temperature. 

286. Rules for the Care of Mercurial Thermometers. — 
The following rules for handling and using mercurial thermome 
ters, if carefully observed, will reduce accidents to a minimum : 

1. Keep the thermometer in its case when not in use. 

2. Avoid all jars ; exercise especial care in placing in ther- 
mometer-cups. 

3. Do not expose the thermometer to steam heat unless 
the graduations extend to or beyond 350 F. 

4. In measuring heat given off by working-apparatus, or in 
continuous calorimeters, do not put the thermometers in place 
until the apparatus is started, and take them out before it is 
stopped. Be especially careful that no thermometer is over- 
heated. 

5. In general do not use thermometers in apparatus not 
fully understood or which is not in good working condition. 

6. Never carry a thermometer wrong end up. 

7. See that the thermometer-cups are filled with cylinder- 
oil or mercury. If cylinder-oil is used, keep water out of the 
cups or an explosion will follow. 



§288.] MEASUREMENT OF TEMPERATURE. 37 1 

8. After a thermometer is placed in a cup, keep it from 
contact with the metal by the use of waste. 

287. Alcohol-thermometers. — Other liquids, as alcohol 
-or spirits of wine, are better suited for low temperatures than 
mercury, but on account of the tension of their vapors are not 
suited for high temperatures, and are probably subject to the 
same objections in a less degree as mercurial thermometers. 

288. Air-thermometers. — Air-thermometers,in which either 
air or hydrogen may be used, are not open to the objections 
which hold with the mercurial thermometer, as the expansion for 
uniform increments of heat is under all conditions the same. 

There are two plans of these thermometers : 
I. Increase of volume of air at constant presssure. 

II. Increase of pressure at constant volume. 

The latter plan was found to give better results by Reg- 
nault, and constitutes the principle of the " Normal Air-ther- 
mometer." 

The air-thermometer in construction is a U-shaped tube, 
one branch enlarged into a bulb for the air, the other open for 
the mercury. Adjacent to the tube for the mercury is a gradu- 
ated scale which can be read by a vernier to small divisions of 
an inch ; a single mark is placed in the air branch, at a dis- 
tance of eight or ten inches from its top. This mark serves to 
define the limit of volume used. 

There are various forms of instrument in use ; the one 
adopted at Sibley College was designed by Mr. G. B. Preston 
and is shown in Fig. 180. The air-bulb, C, is approximately 
if inches by 6 inches ; the bulb is joined by a capillary tube, F, 
straight or bent into any convenient form as may be required* 
In order that the bulb may be conveniently located for heat- 
ing, this capillary tube is joined to a tube of glass about -^inch 
bore, the end of which is bent at right angles ground true, and 
joined by a short piece of rubber tubing to a glass tee at B. 
The tee has a branch provided with a cock, and connection for 
rubber tubing. The opposite side of this tee is joined in a 
similar way to a tube, BE, of the same bore, which is given a 
length sufficient to measure the required temperatures. A mark 



372 



EXPERIMENTAL ENGINEERING. 



[§28& 



a is made on the glass near F, at the junction of the capillary 
tube with the larger one for the mercury, and serves to deter- 
mine the limit of volume of air used. The bottle, A\ is filled 
with mercury, and connected by a rubber tube to the cock B. 
By opening the cock and elevating the bottle, mercury will 



v^ / y/y^ /// /// //y//^///^////////////// ( 



< 



y//y///yyy^yyy/y/yyy^yy^y^^^ 




Fig. i8o.-— Preston Air-thermometer. 

pass into the tubes : when it reaches the height of the mark a f 
the connecting cock B is closed, and the amount that the col- 
umn BE extends above the level of this mark, or fails of 
reaching this level, is read on the scale. 

Hoadley Air-thermometer. — The Hoadley air-thermome- 
ter, as described in the Transactions of the American Society of 
Mechanical Engineers, Vol. VI., page 282, is shown in Fig. 181, 
with all the dimensions marked. It differs from the preceding 
one in having no means provided for introducing or removing 
mercury to maintain the volume of air constant. The tube con- 
nected to the air-bulb, instead of being capillary, is about 
-ig- inch diameter. The instrument consists of a U-tube about 



§ 288.] 



MEASUREMENT OF TEMPERATURE. 



373 



§ inch external diameter, -^ bore, having a 
short leg about 39 inches long, and the other 
leg longer by 12 inches or more, the latter sur- 
mounted by a bulb blown out of the tube if 
inches in diameter, 6f inches in extreme length. 
The branches of the U-tube are 2 inches apart 
and vertical ; these are separate tubes, each one 
bent to a right angle by a curve of short 
radius, ground square and true at the ends 
and united by a short coupling of rubber 
tubing, ea, firmly bound on each branch with 
wire. After it is filled with dry air according 
to the directions in Article 290, page 376, it is 
fastened on a piece of board by annealed wire 
staples, and paper scales affixed as shown in 
the figure. The difference in height of .the £ 
two columns of mercury is taken as the read- I 
ing of the thermometer, and no correction is % 
made for slight variations in the volume of I 
air, as shown by variation in the position of the 1 
height of the mercury column in the branch < 
BC. The error caused in this way is very small | 
and amounts to only 0.0030 inch per inch of \ 
height. This is equivalent to an error of about ■§ 
five degrees in a range of temperature of 600 § 
degrees F. J 

The Jolly Air-thermometer . — An exceedingly J 
simple form of the air-thermometer, and one also [ 
very accurate, consists of the air-bulb C, and a I 
capillary stem attached to three or four feet | 
of rubber tubing, which replaces the U-tube js 
in Fig. 180; in the other end of the rubber 
tubing is inserted a piece of glass tube 8 to 12 
inches long and about -^ inch bore ; on this 
glass tube, and also on the capillary tube, is 
etched a single mark ; the rubber tube is filled 
with mercury, which extends up the glass tube p IG# 
on the other branch. A fixed scale, similar to DE £J 



X 



«• 



x 1 * I 



1 

n> 








F 


1" 


2* 


D 


G 




'di. 


C 


c 


'-16 
-M 

-14 
-13 

-12 
-11 
-10 
-8 
-8 

-C 
-5 
-4 

-3 

—2 


c 


r 1 


hi 


I ~c 


3 






3 






5 ~J 






3 






3 






3 






n-jj 






12J 






13 j1 






14J 






15-1 






10-J 






17 ' 


!$]QB£ 


' H 



-0 e 



t8i.— The Hoad- 

AlR-THERMOM- 



374 



EXPERIMENTAL ENGINEERING. 



[§ 28 9 . 



in Fig. 181, is located near the instrument. To use the instru- 
ment the tube is manipulated until the air is brought to its 
limit of volume, then the other end of the tube is held oppo- 
site the scale, and the reading corresponding to the height of. 
the mercury is taken. This is repeated for several tempera- 
tures, and, if the constant of the instrument is known, gives the 
data for computing the temperature. 

289. Formulae for the Air-thermometer of Constant Vol- 
ume. — The pressure exerted by the confined air, added to the 
weight of mercury, in the branch Bfr, Fig. 180, will equal the 
weight of mercury in the other branch plus the weight of the 
atmosphere. Thus let p equal the pressure expressed in inches 
of mercury of the confined air, v its volume, tn the height of 
the mercury in the branch of the tube on the side of the air- 
bulb, m! the height in the other branch, b the pressure of the 
atmosphere expressed in inches of mercury, T the absolute 
temperature, t the thermometer-reading, h the height of mer- 
cury in the tube BE above the mark a, no mercury being 
above the point a in the tube BF. Let a equal constant ratio 
of T to pv. Then we have, since the pressures in both branches 
of the tube are equal, 

p -j- m z=£ m! -\- b\. ...... (1) 

p = m' — m -f- h. 

Since m* — m = k, . (2) 

P = h + t. (3) 

From physics, 



pv 
T 



-=, = constant 



(4) 



£289.] MEASUREMENT OF TEMPERATURE. S7 5 

and if v be made constant,/ will vary as T; also 

T= 4 6o f /; ,. (5) 

p = Z(constant) = (460 + t)a ; .... (6) 
hence 

{ A 6o + t)a = b + k (7) 



Let the same symbols with primes denote other values of the 
corresponding quantities. Then 



(460 + t')a = b' + k r (8) 

By comparing equations (7) and (8), 

460 -f- 1 _ b + h 

4 6o + f ~ V + ti W 

From which, by solving, 

T+T (46 ° + ^J ~ 46 ° (l °) 



f = 



To apply the formula, take readings of the instrument at 
32 F., or some known temperature, and ascertain the con- 
stants of the instrument. Thus suppose the air-bulb to be 
packed in ice and the temperature reduced to 32 F. In this 
case t = 32 ; b and h are to be observed and recorded. 



37 '6 EXPE RIM EN TA L ENGINEERING. 

If / = 32° in equation (10), 



[§ 290. 



t' = ^r h ib' + h')- A ^ 



(II) 



which is an equation to determine any temperature. If b and h 
are constant, 492 ~ {b -\- h) is constant and equals K. 



t = K(b / + /i / )-46o; 



(12) 



which is the practical equation for use in determining tem- 
peratures. 

If the height of the mercury in the column EB, Fig. 180, 
is less than that in FB, h will be negative, and is to be so con- 
sidered in the preceding formulae. 

In the use of the air-thermometer the mercury must be 
maintained constantly at the point a in the branch FB; this 
will require the addition of mercury to the U-tube as the press- 
ure increases, which -is readily done by raising the bottle A 
and opening the connecting-cock B. By a reverse process 
mercury may be removed as the pressure decreases. 

290. Construction of the Air-thermometer. — The bulb 
of the air-thermometer must be filled with perfectly dry air, 
as any vapor of water will vitiate the results. 

To accomplish this, the bulb is provided with a small open- 
ing opposite the capillary tube, which is fused after the dry air 
is introduced. To effect the introduction of dry air, all the 
mercury is drawn into the bottle A, Fig. 180; the end of 
the tube E is connected to a U-tube about 6 inches long in 
its branches and about J inch internal diameter, filled with dry 
lumps of chloride of calcium and surrounded by crushed ice; 
the opening in the end of the air-chamber is connected by a 
rubber tube to an aspirator (a small injector supplied with 
water would act well as an aspirator), and air is drawn through 



§292.] MEASUREMENT OF TEMPERATURE. 377 

for three or four hours: at the end of this time the bulb and 
tube should be filled with dry air. While the current of air is 
still flowing, the cock B is opened and mercury allowed to pass 
into the tubes until it rises to the point a in the tube BF; the 
opening in the air-chamber is then hermetically sealed with a 
blow-pipe, and the connections to the chloride-of-calcium tube 
removed. This operation fills the bulb with air at atmospheric 
pressure. By closing the cock B before the mercury has risen 
to the point a the pressure will.be increased ; by closing it after 
it has passed the point a it will be diminished. Packing the 
bulb C in ice, or heating it, will also increase or diminish the 
pressure as required. 

291. Corrections to Determinations by the Air-thermom- 
eter. — The corrections to the air- thermometer are all very 
small, and affect the results but little if considered. They are : 

1. Capillarity, or adhesion of the mercury to the glass. In 
general the mercury in the two tubes j5.Fand BE (Fig. 180) is 
moving in opposite directions, and the effect of adhesion is 
neutralized. For error in other cases see table on page 351. 

2. Expansion of the glass. This is a small amount, and 
may usually be neglected. The coefficient of surface expan- 
sion of glass is 0.00001 per degree F. ; it is entirely neutralized 
if the column of mercury is not reduced in area at the point 
of meeting the air from the bulb. 

3. Expansion of the mercury should in every case be taken 
into account by reducing all observations to 32 F., the coeffi- 
cient of expansion being 0.0001 per degree F. Reduce all ob- 
servations before applying formulae. 

4. Errors in the fixed scale should be determined and 
observations reduced before applying formulas. 

292. Practical Uses of the Air-thermometer. — The air- 
thermometer may be used as a standard with which to compare 
mercurial thermometers ; in this case the bulb of the air-ther- 
mometer is surrounded with a non-conducting chamber (Fig. 
180), in which the thermometer to be compared is inserted. 
For low temperatures water may be circulated through this 
chamber, and simultaneous readings taken ; for higher tern- 



37 8 EXPERIMENTAL ENGINEERING. [§293. 

peratures steam may be used. Time must in each case be 
given to permit the fluid in the air-thermometer to arrive at 
the true temperature. 

In comparison with mercurial thermometers, an exact 
agreement may be found at freezing and boiling points ; but at 
other places a slight disagreement may be expected, which will 
increase rapidly for high temperatures. 

The air-thermometer may also be used to measure tempera 
tures directly. When the bulb is connected with a long capil- 
lary stem it may be introduced into flues, and temperatures 
below the melting-point of glass measured. The melting 
point will vary from 600 to 800 degrees F. By using porcelain 
bulbs extremely high temperatures can be measured. 

293. Directions for Use of the Air-thermometer. 

First. To obtain the Constants of the Instruments. — Enclose 
the air-bulb with crushed ice, arranged so that the water will 
drain off. Note the reading of the mercury column of the air- 
thermometer h and of the barometer b ; by means of the at- 
tached thermometers reduce these readings for a temperature 
of the mercury corresponding to 32 F. Correct for errors of 
graduation. Divide 492 by the sum of these corrected readings 
for the constant of the air-thermometer. Call this constant K. 

Second. To Measure any Temperature t'. — Note the corre- 
sponding reading of the mercury column k ', and that of a 
barometer b' in the same room. The reading of the mercury 
column plus that of the barometer will correspond to b' -\-h r 
in the formula 

t' = ^Ab' + h') - 460 = K(b' + h') - 460. 

Third. To Compare a Mercurial Thermometer. — Make simul- 
taneous readings of the thermometer when hanging in the 
chamber with the air-bulb, and the height of the mercury 
column. Perform reduction, and plot a calibration curve for 
each io° of graduation. 

Fourth. For general use of the air-thermometer, arrange 



§ 294-] 



MEASUREMENT OE TEMPERATURE. 



379 



the bulb so that it can be inserted into the medium whose 
temperature is to be measured, with the U-shaped tubes in an 
accessible position for reading. Obtain the temperature as 
explained above (see Second). 

294. Form for Reducing Air-thermometer Determina- 
tions. 



TEMPERATURE DETERMINATIONS WITH AIR-THERMOMETER. 

By 189... 

Determination of Constant. 





Symbol. 


I. 


II. 


III. 


IV. 


Temperature of air-bulb 




































Reduced to 32° 


b 


















Thermometer. 












Reduced to 32 . 


h 

A 









































Determination of Temperature. 

t' = K(b' + h') -460. 





Barometer. 


Air-thermometer. 


Z>'+ k' 
Sum. 


t' 
Tem- 
pera- 
ture. 


Mercury 
Thermometer. 


No. 


Read- 
ing. 


Ther. 


b' 
re- 
duced. 


Read- 
ing. 


Ther. 


h' 
re- 
duced. 


Read- 
ing. 


Error. 


I 






















2 






















3 
4 
5 
6 


















































































7 
8 










































9 
10 
































































12 






































1 







3 8o 



EXPERIMENTAL ENGINEERING. 



[§ 2 9 6. 



295. Determination of Boiling and Freezing Points. 

First. To test for Boiling-point.- — Suspend 
the thermometer so that it will be entirely 
surrounded in the vapor of boiling water 
at atmospheric pressure but will not be in 
contact with the water. Note the reading. 
From the barometer-reading calculate the 
boiling-point for the same time. The dif- 
ference will be the error in position of the 
boiling-point. 

The engraving (Fig. 182) shows an in- 
strument for determining the boiling- 
point. The bulb of the thermometer is 
exposed to steam at atmospheric pressure, 
which passes up to the top of the instru- 
ment around the tube, and down on the 
outside, discharging into the air, or it may 
be returned directly to the cup, thus ob- 
viating the need of supplying water. In 
the form shown, the parts telescope into 
each other for convenience in carrying, 
which is entirely unnecessary for labora- 
tory uses. 

Secondly. To test for Freezing-point. — 
Surround the bulb of the thermometer by 
a mixture of water and ice, or water and 
snow ; drain off most of the water. The 
difference between the reading obtained 
and the zero as marked on the thermometer (32 for Fahr. 
scale) is the error in location of freezing-point. 

296. Metallic Pyrometers are instruments used for meas- 
uring high temperatures. The ordinary instruments sold under 
this name are made of two metals which have different rates of 
expansion, copper and iron generally being used. The differ- 
ence in the rate of expansion is employed by means of levers 
and gears to rotate a needle over a dial graduated to degrees. 
In using the metallic pyrometer no reading should be taken 
until it has had sufficient time to arrive at :he temperature of 



Fig. 182. — Apparatus to 
Test boiling-point. 



§ 298.J MEASUREMENT OF TEMPERATURE. 38 1 

the medium in which it is enclosed ; when one tube alone is 
heated, the needle may be stationary on the dial, or even have 
a retrograde motion. 

The metallic pyrometer is usually calibrated by immersing 
in a pipe filled with steam under pressure and comparing the 
temperature with that given by a calibrated mercurial ther- 
mometer. The scale so obtained is assumed to be uniform 
throughout the range of the pyrometer and beyond the limits 
of the calibration. Comparison might be made with an air- 
thermometer. The extreme range of such pyrometers is about 
1200 Fahr., but they are probably of little value for tempera- 
tures exceeding 1000 Fahr. 

Wedgewood's Pyrometer is based on the permanent contrac- 
tion of clay cylinders due to heating. This contraction is 
determined by measurement in a metal groove with plane sides 
inclined towards each other. This pyrometer does not give 
uniform results. 

297. Air-pyrometer. — The air-thermometer with a bulb of 
porcelain, or platinum or other refractory material, affords an, 
accurate method of measuring high temperatures. 

Mr. Hoadley* states that the ordinary air-thermometer made 
of hard glass can be used to determine temperatures of 8oo° 
Fahr. With porcelain bulb it has been used to measure tem- 
peratures of 1900 Fahr. 

298. Calorimetric Pyrometers. — Pyrometers of this class 
determine the temperature by heating a metal or other refrac- 
tory substance to the heat of the medium whose temperature 
is to be measured. Suddenly dropping the heated body into a 
large mass of water, the heat given off by the body is equal to 
that gained by the water ; from this operation and the known 
specific heat of the substance the temperature is computed. 
Thus, let K equal the specific heat of the body, M its weight ; 
let W equal the weight of water, t its temperature before, and 
t' after, the body has been immersed ; let T equal the tempera- 
ture of the heated body, t' its final temperature. Then 

KM{T-f)= W{t' -t). 

* See Vol. VI., Transactions American Society Mechanical Engineers. 



382 EXPERIMENTAL ENGINEERING. [§ 300. 

From which 

W 

In connection with pyrometrical work, the specific heat of 
the substance used often has to be determined. 

299. Determination of Specific Heat. — The specific heat 
of a body is determined by heating it to a known temperature ; 
for instance, after heating it in steam of atmospheric pressure 
until it has attained a known temperature T, its weight M 
having been accurately determined, it is dropped suddenly 
without loss of heat into a vessel containing ^pounds of water 
at a temperature of 6o° Fahr. Let K be the specific heat of 
the body, and t' the resulting temperature. The vessel must 
be so made that there is no loss of heat, and that the water 
can be thoroughly agitated so that an accurate measure of the 
temperature t' can be taken ; also the effect of the vessel in 
cooling the body must be determined and considered a part of 
the weight W. Then will the loss of heat of the body be equal 
to that gained by the water. 

K{T- t')M= W{t' - 6o°). 
From which 

~ m {T—ty 

The specific heat of most bodies is not quite constant but 
is found to increase with higher temperatures. 

300. Values of Specific Heat and Melting-point— 
The metals required for pyrometrical purposes are those with 
a high melting-point and a uniform and known specific heat. 
The obvious losses of heat in (1) conveying the heated body 
to the calorimeter, and (2) radiation of heat from the calorim- 
eter, may be considerable, and should be ascertained by radia- 
tion tests and the proper correction made. Nearly all metals 
are oxydized, or acted on by the furnace-gases, long before the 
melting-point is reached; so that, in general, whatever metal 
is used, it must be protected by a fire-clay or graphite crucible. 
Platinum, copper and iron are usually employed. The following 
table gives determinations of melting-points and specific heats: 



S300.J 



MEASUREMENT OF TEMPERATURE. 



3*3 



TABLE OF MELTING-POINTS AND SPECIFIC HEATS OF 
METALS. 



Metal. 


Melting-point. 


Specific Heat. 
Low Temperatures. 


Degrees 

Fahr. 


Degrees 
Centigrade. 




2900 

3400 
2550 

1870 
700 
630 

493 
426 

- 38 
239 


2000 

415 

325 
264 
228 

425 


. O.034 
0.II8 
O.IIO 
O.14 
O.94 
O.170 
O.094 
0.O93 
O.030 
O.030 
O.O47 
O.030 
0.200 


Steel 


Wrought- iron. ... 


Copper 

Porcelain 


Zinc 


Bismuth 

Tin 


Mercury 


Antimony 



The mean specific heat of Platinum* has been the subject of 
careful investigation. It was found to vary from 0.03350 at 
ioo° C. to 0.0377 at 1 ioo° C. by Poullet, the experiment being 
made with a platinum reservoir air-thermometer. 

The following were the determinations : 



Platinum. 


Copper. 


Range of Temperature. 


Mean Specific 


Range of Temperature. 


Mean Specific 


Degree Centigrade. 


Heat. 


Degree Centigrade. 


Heat. 


O to IOO 


O.03350 


15 to TOO 


O.O9331 


O " 200 


.03392 


16 " 172 


O.09483 


O " 300 


.03434 


17 " 247 


O.09680 


O " 400 


.03476 






O " 500 


•03518 






O " 600 


.03560 






O " 700 


.03602 






O " 800 


. 03644 






O " 90c 


.03686 






O " IOOO 


.03728 






" IIOO 


.03770 







* See Encyclopaedia Britannica, art. Pyrometer. 



384 



EXPERIMENTAL ENGINEERING. 



L§ 301.. 



For zvr ought-iron the true specific heat at a temperature t 
on the Centigrade scale is given as follows by Weinbold : 

C t = 0.105907 + 0.00006538/ + o. 000000066477 f. 

Porcelain or Fire-clay having a specific heat from 0.17 to o.2 r 
although not a metal, is well adapted for pyrometrical purposes. 

301. HoacUey Calorimetric Pyrometer. — The Hoadley 
pyrometer is described in Vol. VI., p. 712, Transactions of 
the American Society of Mechanical Engineers. It consisted 
of a vessel, Fig. 183, made of several concentric vessels of 
copper, with water in the inner one, eider-down in the inter- 
mediate spaces, and a cover of the same nature. Also a sub- 




Fig. 183. — Hoadley Pyrometer. 



stance to be heated consisting of balls of platinum, or wrought- 
hon and copper covered with platinum. These balls were 
heated in a crucible, conveyed to the calorimeter and suddenly 
dropped in. The calorimeter was provided with an agitator 
made of hard rubber, with a hole in the centre for a thermome- 
ter. The balls used as heat-carriers weighed about three quar- 
ters of a pound each ; the vessel held about twelve pounds of 
water. This apparatus is now at Cornell University. 



§ 3Q3-] 



MEASUREMENT OF TEMPERATURE. 



385 



The balls were heated in crucibles and conveyed to the 
calorimeter in a fire-clay jar as shown in Fig. 142. The cover 




Fig. 183. — Platinum Balls and Crucible. 

of this jar was quickly removed and the balls dropped into the 
water in the calorimeter. 

302. Electric Pyrometers. — The fact that electric currents 
are excited by differences of temperature in different parts of 
a metallic circuit is made use of for measuring large as well as 
small differences of temperature. 

The electromotive force of a circuit at different tempera- 
tures is given by Professor Tait* as 

E = A(t l -t,)[T-U.t l + t,)l 

in which E = electromotive force ; T, a constant temperature, 
such that no current is produced if temperatures on either side 
are equal, and which depends on the metal : for copper and 
iron it is about 284 C. A is a constant depending on the 
metals ; t 1 = the higher temperature, t 2 the lower. 

303. Siemens's Pyrometer. — This instrument is based on 
the well-known principle of increase of resistance with rise of 
temperature. 

The formula given by Siemens for the resistance of metals is 

R=aVT+/3T+y; 



* See article Pyrometer, Encyc. Britannica. 



3&6 EXPERIMENTAL ENGINEERING. [§ 304. 

in which R equals the resistance to be measured, a, 0, and y 
are coefficients, and T equals the absolute temperature. 

The resistance is ascertained by a volt-meter, and the co- 
efficients a, fi, and y are determined by special calibration. 
The heated substance is a platinum wire wound around a clay 
cylinder and protected by a covering of fine clay; this is in- 
serted into the furnace or medium whose temperature is 
required. The current is passed alternately in different direc- 
tions, and the resistance is measured by the gas accumulating 
in a volt-meter at either pole. 

The instrument is very sensitive to slight changes of tem- 
perature, and is well suited for accurate measurements of 
moderate temperatures. In the measurement of high tem- 
peratures considerable difficulty was experienced because of 
change in the coefficients due to the extreme heat. 

Callendar's platinum thermometer is an electrical pyrometer 
of the resistance type arranged so that one portion is maintained 
at constant temperature by being kept in a vessel of water contain- 
ing melting ice, while the other part is subjected to the tempera- 
ture to be measured. The difference in resistance of these two 
parts affords a basis for determining the temperature. This 
apparatus is exceedingly accurate and capable of measuring 
very small subdivisions of a degree. 

Professor Brown of McGill University has devised a form of 
the Callendar instrument in which the difference of temperature 
is determined by equalizing the resistance through two circuits 
until they are the same, which fact is indicated by the use of a 
telephone which transmits no sound at that instant. 

304. Optical Pyrometers. — From the fact that the color of 
an incandescent body varies with the wave length and this again 
with the temperature, it is possible to determine the temperature 
of such bodies by theii appearance. 

For ihis purpose a number of optical pyrometers have been 
devised. The Mesure and Nouel's pyrometric telescope meas- 
ures the temperatures by taking advantage of the rotation of the 
plane of polarization of light passing through a quartz plate cut 



§ 304-] 



MEASUREMENT OF TEMPERATURE. 



387 



perpendicular to its axis. The angle of rotation is directly pro- 
portional to the thickness of the quartz, and approximately in- 
versely proportional to the square of the wave length. 

Light from an incandescent object, passing through the 
slightly ground diffusing-glass G (Fig. 185), enters a polarizing 




Fig. 185. — Mesure and Nouel Pyrometric Telescope. 

nicol P, and, traversing the quartz plate Q, strikes the analyzer A, 
and is seen through the eye piece OL. 

In the use of the instrument the analyzer is turned until the 
object appears to have a lemon-yellow color. The position of 




'-■ Fine =f3 

f 



JIilli_Ammeter 

Fig. 186. — The Morse Thermo-gauge. 



the analyzer is indicated by the graduated circle C, the reading 
of which may be referred to a temperature scale. Because of 
the variations due to personal errors of different observers the 
uncertainties of observations are likely to amount to fully ioo° C. 
The instrument is very convenient for use and is approximately 
accurate. 



388 



EXPERIMEN TA L ENGINEERING. 



[§ 304. 



The Morse thermo-gauge is shown in Fig. 186. It employs 
an incandescent lamp with a rheostat arranged so that the current 
flowing through it and its consequent brightness may be regu- 
lated. The amount of current flowing through is shown by a 
milli-voltmeter connected in circuit, the reading of which can be 
referred to a scale for the determination of temperature. The 
lamp is adjusted from an experimental scale for its degree of 
brightness at different ages. 

In using this instrument the incandescent lamp is located 
between the eye and the object whose temperature is to be meas- 
ured, and the current is regulated until the lamp is invisible. This 
instrument is designed for use in hardening steel and has an 
extensive use in that industry. 

General Remarks regarding Pyrometers. — An ex- 
tended series of experiments with the different pyrometers 
described has led the author to believe that the calorimetric 
forms, as described in Articles 298 and 301, despite their in- 
convenience and the losses from radiation which attend their 
use, give, if we except the air-pyrometer, more uniform and re- 
liable results than the others. The electrical pyrometers are 
subject to the same inaccuracy as the calorimetric pyrometers, 
due to complex changes in the electrical resistances of the 
thermometric substance, so that the results are quite uncer- 
tain for high temperatures. 

The electrical pyrometers also need for their successful 
use a command of electrical energy and the possession of a set 
of electrical measuring instruments. While these pyrometers 
may give reliable results with skilled electricians, they are of 
little practical use to the engineer. The calorimetric pyrom- 
eters are cheap, portable, and easy to use, and with careful 
handling give uniform and fairly reliable results. The best 
substance for use in these instruments as a heat-conveyer is, 
in the opinion of the author, a porcelain or fire-clay ball 
about 2 inches in diameter. The metals, not even excepting 
platinum, are readily attacked by the furnace-gases, and when 



i 304.] 



MEASUREMENT OF TEMPERATURE. 



389 



employed need to be protected in a crucible of refractory 
material. If used by heating directly in the furnace, wrought- 
iron is perhaps as good as any of the metals. It may be oxi- 
dized and fall in pieces" but since the oxide has about the same 
specific heat as the original metal, determinations may be made 
with the residue without any great error. The porcelain or 
fire-clay balls seem to be unaffected by the furnace-gases, and 
do not radiate heat as rapidly as the metals, so that were the 
specific heat as accurately determined they would be superior 
in every way to the metallic balls. The determination of the 
specific heat of burned fire-clay as made by Mr. D. J. Jenkins 
at Sibley College was 0.1702 at temperature of boiling water. 
By comparison with results obtained with a metal 
whose specific heat was known, the specific heat 
at 1000 C. (1832 F.) is calculated as about 0.20. 
The latter quantity is subject to correction. 

The air -py- 
rometer with a 
porcelain or plat- 
inum bulb can be 
used convenient- 
ly, and the cor- 
responding tem- 
peraturesso read- 
ily and easily 
deduced from the 
determinations 
that it is worthy 
a much more ex- 
tended use. The 
bulb may be 
made in any de- 
sired form and Element op Le Chatelier's Pyrometer. 

a long capillary stem can be led from the bulb to the meas- 
uring tubes a long distance without sensible error, so that it 
may be adapted to a variety of uses. 




Le Chatelier's Electrical Pyrometer. 




CHAPTER XIII. 

METHODS OF DETERMINING THE AMOUNT OF MOISTURE 

IN STEAM. / 



305. Quality of Steam. — Degree of Superheat, — Steam 
may be dry and saturated, wet or superheated, as described in 
Article 265, page 340. The term quality is used to express 
the relative condition of the steam as compared with dry and 
saturated steam of the same pressure. It is in any case the 
total heat in a pound of the sample steam, less the heat of the 
liquid, divided by the total latent heat of evaporation of one 
pound of dry steam at the same pressure, see page 343. 

For moist or wet steam, which is to be considered as made 
up of a mixture of water and dry steam, the quality would 
equal the percentage by weight of dry steam in the mixture. 

For superheated steam the quality would exceed unity, and 
is to be considered as that weight of dry and saturated steam, 
the heat in which is equivalent to that in one pound of the 
superheated steam, neglecting in both cases the heat of the 
liquid. 

In case of superheated steam, its temperature is higher 
than that of dry and saturated steam at the same pressure ; 
this excess of temperature is termed degree of superheat. 

306. Importance of Quality Determinations. — The im- 
portance of correctly determining the quality of steam is great, 
because the percentage of water carried over in the steam in 
the form of vapor or drops of water may be large, and this 
water is an inert quantity so far as its power of doing work is 
concerned, even if not a positive detriment to the engine. Any 
tests for the efficiency of engine or boiler not accompanied 
with determinations of the amount of water carried over in the 

390 



§ 309-] 



THE AMOUNT OF MOISTURE IN STEAM. 



391 



steam would be defective in essential particulars, and might 
tead to erroneous or even absurd results. 

307. Methods of Determining the Quality. — The methods 
of measuring the amount of moisture contained in steam may 
be considered under three heads: first, Calorimetry proper ; in 
which the method is based on some process of comparing the 
heat actually existing in a pound of the sample with that 
known to exist in a pound of dry and saturated steam at the 
same pressure. Secondly, Mechanical Separation of the water 
from the steam, involving the processes of separation and of 
weighing. Thirdly, a Chemical Method, in which case a soluble 
salt is introduced into the water of the boiler. This salt is not 
absorbed by dry steam, and if it is found in the steam it indi- 
cates the presence of water. The quality is equal to the ratio 
of salt in the steam to that in an equal weight of water drawn 
from the boiler. 

All methods for determining the quality of steam are 
included under the head of calorimetry , and instruments for 
determining the quality are termed calorimeters. 

308. Classification of Calorimeters. — The following clas- 
sification of different forms of calorimeter is convenient and 
comprehensive: 



[Jet. 



Calorimeters 



' Condensing 



Superheating. 



Surface 



Barrel or Tank. 
Continuous. 

Barrus — Continuous. 
Hoadley Calorimeter. 
Kent — Tank Calorimeter. 



External — Barrus Superheating. 
Internal — Peabody Throttling. 



L Directly determining moisture \ c^m^ah 



309. Error in Calorimetric Processes. — The calorimetric 
processes proper depend on the method of measuring the heat 
actually existing in a pound of the sample steam at a known 
pressure. This measurement is then compared with the re- 
sults given in a steam-table for dry and saturated steam, and 
the quality is computed as will be explained later. 



392 



EXPERIMEN TA L ENGINEERING. 



[§3io. 



In nearly every calorimetric process the heat of the sample 
is determined by condensing the steam at atmospheric press- 
ure, or at least measuring the heat when its conditions of 
pressure and temperature are different from its original state. 
This process involves no error. The following is a statement of 
an investigation concerning it made by Sir William Thomson:* 

" If steam have to rush through a long fine tube or 
through a fine aperture within a calorimetric apparatus, its 
pressure will be diminished before it is condensed ; and there 
will, therefore, in two parts of the calorimeter be saturated 
steam at different temperatures; yet on account of the heat 
developed by the fluid friction, which would be precisely the 
equivalent of the mechanical effect of the expansion wasted in 
the rushing, the heat measured by the calorimeter would be 
precisely the same as if the condensation took place at a press- 
ure not appreciably lower than that of the entering steam." 

310. Use of Steam-tables. — In reducing calorimetric ex- 
periments steam-tables will be required. The explanation of 
the terms used will be found in Article 265, page 340, and 
tables will be found in the Appendix of the book. 

Students will please notice, that the pressures referred to in 
the steam-tables are absolute, not gauge pressures, and that 
gauge pressures are to be reduced to absolute pressures, by 
adding the barometer-reading reduced to pounds per square 
inch, before using the tables. 

The following symbols will be employed to represent the 
different properties of steam : 

TABLE OF SYMBOLS. 



Properties of Steam. 


Symbol. 


Properties of Steam. 


Symbol. 


Pressure, pounds per sq. in. 
Pressure, pounds per sq. foot 
Temperature, degrees Fahr. 
Temperature absolute 


P 

P 

t 

T 

q or S 

p or I 

APuor E 

r or L 


Total heat B. T. U 

Weight of cu. ft. of steam lbs. 
Vol. of 1 lb. steam, cubic ft. 
Vol. of 1 lb. water, cubic ft . 
Change in volume v — o~ . . . 
Quality of steam 


Xor H 
8 or W 
v or C 

cr 

u 






External latent heat 

Total latent heat 


Per cent of moisture 

Degree of superheat 


I — X 

D 







* Mathematical Papers, XLVIIL, p. 194. 



§ 3 I2 THE AMOUNT OF MOISTURE IN STEAM. 393 

The quantities q, p, APu, r, and A are given in B. T. U. 
per pound of saturated steam reckoned from 32 Fahr. 

311. General Formula for the Heat in One Pound of 
Steam. — The heat existing in one pound of steam with any 
quality x can be expressed by the formula 

xp-\-q — h. (1) 

The heat, however, which is required to raise water from 
32 F. and convert it into steam at a given temperature will 
include the external latent heat, and will be expressed by the 
formula 

xr-\-q = h'. . . . . . . . (2) 

The heat that may be given out by condensation or change 
of pressure is expressed in equation (2) ; that which exists in 
the steam without change of pressure or external work, by 
equation (1). 

Since in all calorimetric processes the steam is condensed, 
or at least the pressure changed, equation (2) is to be employed 
to represent the available heat. 

If the pressure of the steam is known, r and q can be found 
from the steam-tables. If the heat h in B. T. U. above 32 
can be found for the sample steam, all the quantities in the 
above equation with the exception of x are known, and we 
shall find 

x = — — *. ....... (3) 

In case x is greater than unity, the steam is superheated, and 
the degree of superheat 

"-^ «> 

when 0.48 equals the specific heat of steam, c p . 

312. Methods of Determining the Heat in a given 
Sample of Steam. — There are two methods of determining 
the heat h in a given sample of steam. 



394 EXPERIMENTAL ENGINEERING. [§ 312. 

I. Condensing the Steam at Atmospheric Pressure. — In this 
case the weight of the steam is obtained by weighing the con- 
densing water before and after condensation has taken place 
and determining the corresponding temperatures. Thus let 
the weight of condensing water be represented by W, that of 
the condensed steam by w; the temperature of the condensing 
water cold by t 1 , the condensing water warm by / 2 ; the original 
temperature of the steam by t } that of the condensed steam by 
t % . Suppose that the calorimeter absorb heat to the same 
extent as k pounds of water; then the heat added by con- 
densing one pound of steam is equal to 

^«.-<.> » 

The original heat above 32 from equation (2), page 363, 
is xr-\-q. Since in equation (5) the temperature is reck- 
oned above zero, it will be more convenient to use, instead of 
xr-\- q-\- 32, xr -\- t, which is very nearly identical. 

Since the heat lost in condensing one pound of steam is 
equal to that gained by the water, we shall evidently have 



from which 

W+k{t-t) (t-t t ) 



x = 



w r r 



(6) 



If the temperature of condensed steam equal that of the 
warm condensing water, t % = t 2 , which is the usual condition of 
condensation. 

2. Superheating the Steam. — If the pressure and tempera- 
ture of superheated steam is known, the degree of superheat D 
can be found by deducting the normal temperature, as given 
in the steam-table for that pressure, from the observed tem- 
perature. The total heat in a pound of the superheated steam 



§ S l 3-] THE AMOUNT OF MOISTURE IN STEAM. 395 

is equal to that in a pound of saturated steam, as given by the 
steam-tables, plus the product of the degree of superheat into 
the specific heat c P of the steam ; that is, 

H = X + c p D. 

The superheating may be done by extraneous means, as in 
the Barrus superheating calorimeter, or by throttling, as in 
the throttling calorimeter. In the latter the heat required for 
superheating is obtained by reducing the pressure, which, being 
accompanied by a corresponding reduction of boiling point, 
liberates heat sufficient to evaporate a small percentage of 
moisture only. 

In the case of the superheating calorimeter, the heat re- 
quired to evaporate the moisture and superheat the steam is 
measured by the loss of temperature n in an equal weight of 
superheated steam, so that 

c p n = r(i — x) -f- c p D ; 
«-* = *fe^ (7) 



In the case of the throttling calorimeter there is no change 
in the total amount of heat, but there is a change of pressure, so 
that the quantities in the first member of (8) correspond to the 
original pressures of steam before throttling, and those in the 
second member to the calorimeter pressures after throttling, and 

xr + g=*K + c& x= X <-4 + c > D . . . (8) 



313. Condensing Calorimeters. — Condensing calorimeters 
are of two general classes : 1. The jet of steam is received by 
the condensing water, and the condensed steam intermingles 
directly with the condensing water. 2. The jet of steam is 
condensed in a coil or pipe arranged as in a surface condenser. 



39 6 EXPERIMENTAL ENGINEERING. [§ 314. 

and the condensed steam is maintained separate from the con- 
densing water. 

The principle of action of both classes of condensing calo- 
rimeter is essentially the same, and is expressed by equation 
(6): 

w+ H*,-ti C-'O 

w r / r 



In the first class t s = / 3 , and 



x _ W +k(t- tl ) (t-t,) ( 



W 



Both forms of condensing calorimeter can be made to act con- 
tinuously or at intervals, and there are several distinct types of 
each. 

The most common type of condensing calorimeter is one 
in which the condensing water is received in a barrel or tank, 
and hence is termed a barrel calorimeter. The special forms 
will be described later. 

314. Effect of Errors in Calorimeter Determinations. 

First. Condensing Calorimeters. — To determine the effect 
of error, suppose in each case the quantity under discussion to 
be a variable and differentiate the equation 



W 

£(/,-0-(/-« 

jr = — 



We have 



Ax -T- A W — (/, — O -f- wr ; 

Ax -T- Aw = — ( W~- w 2 ) (t % — *,) -J- r : 

Ax + At, =£(JP-*-«0 + i]-i-r; 

Ax h- At^ = W -f- wr. 



§ 3I4-] 



THE AMOUNT OF MOISTURE IN STEAM. 



397 



Since Ar — — At, nearly, for ordinary pressures of steam, and 
further is a function of the pressure, we have approximately 

Ap = Ap =z — Ar ; 

Ax+Ap = [^(^-0 -t-r + t^r\ 

The weight of condensing water usually held by the barrel- 
calorimeters is from 300 to 400 lbs., while the weight of the 
steam condensed varies from 16 to 20 lbs., and the correspond- 
ing temperatures have a range of 50 to yo° F. For these cases 
it will be found that the percentage of error in quality, sup- 
posing other data correct, is approximately the same as the 
percentage of error in the weights. The error in thermometer- 
determination has nearly the same effect, whether made before 
or after the steam has been condensed. For the amounts usu- 
ally employed the error of one fifth of one degree in tempera 
ture has about the same effect as one half of one per cent error 
in weight ; that is, it makes an error of about the same amount 
in the quality of steam. 

The following shows in tabular form the effect of errors 
with condensing calorimeters in which the ordinary weights of 
water and of steam are used : 

TABULATION OF ERRORS. 







Error 


Error 


Error 


•Sc' 

U V 


Error in 


Error in 


in 


in 


in 


u 


Condensing Water. 


Condensed Steam. 


Temperature, 


Temperature, 


Steam- 


Cdo S 






Cold Water. 


Warm Water. 


pressure. 


c • 
"3 >« 


Lbs. 


Per ct. 


Lbs. 


Per ct. 


Degs. 


Per ct. 


Degs. 


Per ct. 


Lbs. 


Perc. 


3 — 


Total wt. 


= 360 lbs. 


Total wt. 


= 20 lbs. 


Temp. 


=50° F. 


Temp. 


=no° F. 


Pr. = 


88 lbs. 




3-€ 


1.0 


0.2 


1.0 


o-53 


1.2 


0.65 


0.60 


7.0 


8.0 


1 2 


1.8 


o-5 


0.1 


05 


0.27 


0.6 


0.30 


0.30 


3-5 


4.0 


0.6 


1.5 


0.40 


0.08 


0.4 


0.18 


o-S 


0.25 


2-5 


3-o 


3-5 


05 


©■3 


0.08 


0.016 


0.08 


0.045 


O.I 


0.05 


0.50 


0.6 


07 


O.I 


Total wt. 


= 300 lbs. 


Total wt. 


= 20 lbs. 






0.25 






1-5 


0.5 


O.I 


O-S 


0.2 








2.2 




*; s 



39 8 EXPERIMENTAL ENGINEERING. [§ 3 1 4. 

In the table, the errors in the various observations ex- 
pressed in the same horizontal line have the same effect on 
the result. 

From the table it is seen, for the given weights, that an 
error of 3.6 pounds in condensing water, of 0.2 pound in com 
densed steam, of 0.53 F. in temperature of cold water, of 0.65 
F. in warm water, or of 7 pounds in steam-pressure will sever- 
ally make an error in the result of 1.2 per cent. Expressed in 
percentages, an error of 1 per cent in weight or 1.2 and 0.6 
per cent in thermometer-readings makes an error in the quality 
of 1.2 per cent. 

The conditions for determination of moisture within one 
half of one per cent require — 

1. Scales that weigh accurately to half of one per cent of 
the quantity to be weighed. 

2. Thermometers that give accurate determinations to 
about one fifth of one degree F. 

3. An accurate pressure-gauge. 

4. Correct observations of the resulting quantities. 

5. Determination of loss caused by calorimeter. 

Secondly. Superheating Calorimeters. — The Barrus Super- 
heating Calorimeter. — In this, if t 3 — t is the gain of tempera- 
ture of the sample steam, and / 2 — t^ is the loss of temperature 
in the superheated steam, we have, neglecting radiation, 

1 — x — o.48[/ a — t x — (t s — 1)~\ -f- r. 

In the Throttling Calorimeter, where the steam is super- 
heated by expanding, we have by equation (7), making c p = 
0.48, 

\ + 0.4SD — q 
x = . 



In either form of superheating calorimeter the effect of an 
error of one degree in temperature is to make an error in x of 
0.06 of one per cent, while an error of 9 in temperature will 
affect the value of x but 0.5 per cent. The boiling-point 



§ 3150 THE AMOUNT OF MOISTURE IN STEAM. 399 

should be correctly determined, however, especially if the 
amount of superheating is small. 

An error in gauge-reading has about, one half the effect on 
the quality of the steam as in the other class of calorimeters. 

315. Method of Obtaining a Sample of Steam. — It is 
usually arranged so as to pass only a very small percentage of 
the total steam through the calorimeter, and it is important 
that this sample shall fairly represent the entire quantity of 
steam. From experiments made by the author, it is quite cer- 
tain that the quality varies greatly in different portions of the 
same pipe, and that it differs more in horizontal than in verti- 
cal pipes. Steam drawn from the surface of the pipe is likely 
to contain more than the average amount of moisture ; that 
from the centre of the pipe to contain less. The better 
method for obtaining a sample of steam is to cut a long 
threaded nipple into which a series of holes may be drilled, 
and screw this well into the pipe. Half-inch pipe is gen- 
erally used for calorimeter connections, and it may be screwed 
into the main pipe one half or three quarters of the distance to 
the centre, with the end left open and without side-perfora- 
tions, as shown in Fig. 187, or screwed three fourths the 



^ PiBO fflllMMM^^H »*• 



Fig. 187. Collecting-nipples. Fig. 188. 

distance across the pipe, a series of holes drilled through the 
sides, and the end left open or stopped, as shown in Fig. 144. 
A lock-nut on the nipple, which can be screwed against the 
pipe when the nipple is in place, will serve to make a tight 
joint The best form of nipple is not definitely determined, 
although many experiments have been made for this purpose; 
a form extending nearly across the pipe and provided with a 





400 



EXPERIMENTAL ENGINEERING. 



[§3l6. 



slit or with numerous holes is probably preferable. When 
the current of steam is ascending in a vertical pipe, the water 
seems to be more uniformly mixed than when descending in 
a vertical pipe or when moving in a horizontal one. There 
, however, considerable variation tor this condition; 



is 



especially if the steam contains more than 3 per cent of water., 

316. Method of Inserting Thermometers. — In the use of 

calorimeters it is frequently necessary to insert thermometers 




Fig. 189. — Steam-thermometer. Fig 190.— Thermometer-cup. 

into the steam in order to correctly measure the temperature. 
For this purpose thermometers can be had mounted in a 
brass case, as shown in Fig. 189, which will screw into a 
threaded opening in the main pipe. 

The author prefers to use instead a thermometer-cup of the 
form shown in Fig. 190, which is screwed into a tapped open- 



§ 3 1 ?-] THE AMOUNT OF MOISTURE IN STEAM. 401 

ing in the pipe. Cylinder-oil or mercury is then poured into 
the cup, and a thermometer with graduations cut on the glass 
inserted. The thermometer-cups are usually made of a solid 
brass casting, the outside being turned down to the proper di- 
mensions and threaded to fit a f-inch pipe-fitting. The inside 
hole is drilled \ inch in diameter, and the walls are left T V inch 
thick. The total length varies from 4J to 6 inches — depending 
on the place where it must be used. In either case it is essen- 
tial that the thermometer be inserted deep into the current of 
steam or water, and that no air-pocket forms around the bulb 
of the thermometer. The thermometer should be nearly ver- 
tical, and as much of the stem as possible should be protected 
from radiating influence. 

If the thermometer is to be inserted into steam of very little 
pressure, the stem of the thermometer can be crowded into a 
hole cut in a rubber cork which fits the opening in the pipe. 
In case the thermometer cannot be inserted in the pipe it is 
sometimes bound on the outside, being well protected from 
radiation by hair- felting; but this practice cannot be recom- 
mended, as the reading is often much less than is shown by a 
thermometer inserted in the current of flowing steam. In the 
use of thermometers, breakages will be lessened by carefully 
observing the directions as given in Article 286, p. 370. 

317. Determination of the Water-equivalent of the 
Calorimeter. — The calorimeters exert some effect on the 
heating of the liquid contained in them, since the inner sub- 
stance of the calorimeter must also be heated. This effect is 
best expressed by considering the calorimeter as equivalent to 
a certain number of pounds of water producing the same 
result. This number is termed the water- equivalent of the 
calorimeter. The water-equivalent, k, can be found in three 
ways : 

1. By computing from the known weight and specific heat 
of the materials composing the calorimeter. Thus let c be the 
specific heat, W c the weight; then 

k = cW c . 






402 EXPERIMENTAL ENGINEERING. [§3 l8 « 

2. By drawing into the calorimeter, when it is cooled down 
to a low temperature, a weighed quantity of water of higher 
temperature and observing the resulting temperature. Thus 
let W equal the weight of water, t x the first and / 2 the final 
temperatures, and k the water-equivalent sought. Since the 
heat before and after this operation is the same, 





(w+ky, = Wt x 


From which 









3. By condensing steam drawn from a quiescent boiler, and 
thus known to be dry and saturated, with a weighed quantity 
of water of known temperature in the calorimeter ; the tempera- 
ture, pressure, and weight of the steam being known. The con- 
ditions are the same as for equation (6), page 394, all the 
quantities being known excepting k. 

By solving equation (6), 

k = — ^ ■ — — W. .... (10) 

For the barrel and jet condensing calorimeters generally, t % = / 2 , 
and we have 



k _ w{rx + t — / 3 ) 



W. 



The cooling effect of superheating calorimeters is generally 
expressed in degrees of temperature in the reading of one of 
the thermometers. 

SPECIAL FORMS OF CALORIMETERS. 

318. Barrel or Tank Calorimeter. — The barrel calorim- 
eter belongs to that class of condensing calorimeters in which 
a jet of steam intermingles directly with the water of conden- 
sation. It is made in various ways ; in some instances the 



§ 3!8.] THE AMOUNT OF MOISTURE IN STEAM. 



403 



walls are made double and packed with a non-condensing 
substance, as down or hair-felting, to prevent radiation, and 
the instrument is provided with an agitator consisting of 
paddles fastened to a vertical axis that can be revolved and 
the water thoroughly mixed ; but it usually consists of an ordi- 
nary wooden tank or barrel resting on a pair of scales, as 
shown in Fig. 191. 




Fig. 191. — The Barrel Calorimeter. 

A sample of steam is drawn from the main steam-pipe by 
connections, as explained in Article 315, page 369, and con- 
veyed by hose, or partly by iron pipe and partly by hose, to 
the calorimeter. In the use of the instrument, water is first 
admitted to the barrel and the weight accurately determined. 
The pipe is then heated by permitting steam to blow through 
it into the air ; steam is then shut off, the end of the pipe is 
submerged in the water of the calorimeter, and steam turned 
on until the temperature of the condensing water is about 1 io° 
F. The pipe is then removed, the water vigorously stirred, the 
temperature and the final weight taken. If the effect of the 
calorimeter, k, expressed as additional weight of water, is 
known, the quality can be computed as in equation (6), page 394. 

,=^±i*to_&=^. . . . (6) 

wr 7 J 



404 EXPERIMENTAL ENGINEERING. L§ 3 J ^ 

A tee screwed crosswise of the pipe, as shown in Fig. 189, 
forms an efficient agitator, provided the temperature be taken 
immediately after the steam is turned off. 

The pipe may remain in the calorimeter during the final 
weighing if supported externally, and if air be admitted so that 
it will not keep full of water ; in such a case, however, it should 
also be in the barrel during the first weighing, or else the final 
weight must be corrected for displacement of water by the 
pipe. The effect of displacement is readily determined by 
weighing with and without the pipe in the water of the calo- 
rimeter. 

The determination of the water-equivalent of the barrel 
calorimeter will be found very difficult in practice, and it is 
usually customary to heat the barrel previous to using it, and 
then neglect any effect of the calorimeter. This nearly elimi- 
nates the effect of the calorimeter. The accuracy of this 
instrument, as shown in Article 314, page 397, depends prin- 
cipally on the accuracy with which the temperature and the 
weight of the condensed steam are obtained. The conditions 
for obtaining the temperature of the water accurately are 
seldom favorable, as it is nearly impossible to secure a uniform 
mixture of the hot and cold water; the result is that deter- 
minations made with this instrument on the same quality of 
steam often vary 3 to 6 per cent. From an extended use in 
comparison with more accurate calorimeters, the author would 
place the average error resulting from the use of the barrel 
calorimeter at from 2 to 4 per cent. 

Example. — Temperature of condensing water, cold, ^,is 
52°.8 F.; warm, / 2 , I09°.6 F. Steam-pressure by gauge, 79.7; 
absolute, 94.4. Entering steam, normal temperature, from 
steam-table, t, 323°.5 F. Latent heat, r y 888.2 B. T. U. 
Weight of condensing water cold, W, 360 pounds ; warm, 
W-\-w t 379.1 pounds, wet steam, w, 19.1 pounds. Calorim- 
eter-equivalent eliminated by heating. The quality 

^60 (1096- 52.8) _ 323.5 - 1 09.6 = 
19. 1" 888.2 888.2 yi> ' 4 ' 



§ 320.] THE AMOUNT OF MOISTURE IN STEAM. 405 

319. Directions for Use of the Barrel Calorimeter. — 

Apparatus. — Thermometer reading to \ degree F., range 32 
to 212 ; scales reading to -^ of a pound ; barrel provided with 
means of filling with water and emptying ; proper steam con- 
nections ; steam-gauge or thermometer in main steam-pipe. 

1. Calibrate all apparatus. 

2. Fill barrel with 360 pounds of water, and heat to 130 
degrees by steam ; waste this and make no determinations for 
moisture. This is to warm up the barrel. 

3. Empty the barrel, take its weight, add quickly 360 
pounds of water, and take its temperature. 

4. Remove steam-pipe from barrel ; blow steam through it 
to warm and dry it ; hang on bracket so as not to be in contact 
with barrel ; turn on steam, and leave it on until temperature 
of resulting water rises to no° F. Turn off steam; open air- 
cock at steam-pipe as explained. 

5. Take the final weights with pipe in barrel, in same po- 
sition as in previous weighings ; also take weights with the pipe 
removed : calculate from this the displacement due to pipe, and 
correct for same. 

Alternative for fourth and fifth operations. — Supply steam 
through a hose, which is removed as soon as water rises to a 
temperature of no° F. Weigh with the hose removed from 
the barrel. Stir the water while taking temperatures. 

6. Take five determinations, and compute results as ex- 
plained. Fill out and file blank containing data and results. 

7. Compute the value of the water-equivalent, k, in pounds 
by comparing the different sets of observations. 

320. The Continuous-jet Condensing Calorimeter.— 
A calorimeter may be made by condensing the jet of steam in 
a stream of water passing through a small injector or an equiva- 
lent instrument. The method is well shown in Fig. 193. A 
tank of cold water, B, placed upon the scales R, is connected 
to the small injector by the pipe C; the injector is supplied 
with steam by the pipe S, the pressure of which is taken by 
the gauge P; the temperature of the cold water is taken at e, 
that of the warm water at g. Water is discharged into the 



406 



EXPERIMENTAL ENGINEERING. 



[§ 320. 



weighing-tank A, The amount taken from the tank B is the 
weight of cold water W; the difference in the respective 
weights of the water in tanks A and B is the weight of the 
steam w. 

The quality is computed exactly as for the barrel calorim- 
eter. 

In case an injector is used, as shown in Fig. 192, the tank 
B is not needed : water can be raised by suction from the tank 
A through the pipe d. The original weight of A will be that 




Fig. 19a.— The Injector Calorimeter. 

of the cold water ; the final weight will be that of steam added 
to the cold water. 

In case an injector is not convenient, and the water is sup- 
plied under a small head, a very satisfactory substitute can be 
made of pipe-fittings, as shown in Fig. 193. In this case, steam 
of known pressure and temperature is supplied by the pipe A 
cold water is received at S', and the warm water is discharged 
at vS. The temperature of the entering water is taken by a 
thermometer in the thermometer-cup T\ that of the discharge 
by a thermometer at T. The steam is condensed in front of 
the nozzle C. 

This class of instruments present much better opportunities 
of measuring the temperatures accurately than the barrel 
calorimeter, and the results are somewhat more reliable. 



§ 32i.] 



THE AMOUNT OF MOISTURE IN STEAM. 



407 



In the use of continuous calorimeters of any class, the in- 
strument should be put in operation before the thermometers 
are put in place or any observations taken. The poise on the 
weighing-scale can be set somewhat in advance of its bal- 
ancing position, and when sufficient water has been pumped 
out the scale-beam will rise ; this may be taken as the signal 




Fig. 193.— Jet Continuous Calorimeter. 






for saving the water which has been previously wasted, and 
of commencing the run. 

The water-equivalent of the calorimeter, k, will be small, 
and due principally to radiation. It can be found by passing 
hot water through the calorimeter and noting the loss in tern* 
perature. 

321. The Hoadley Calorimeter. — This instrument be^ 
longs to the class of non-continuous surface calorimeters. The 



408 



EXPERIMENTAL ENGINEERING. 



[§ 321. 



instrument is described in Transactions of the American So- 
ciety of Mechanical Engineers, Vol. VI., page 716, and consisted 
of a condensing coil for the steam, situated in the bottom of a 
tank-calorimeter, very carefully made to prevent radiation- 
losses. The dimensions were 17 inches diameter by 32 inches 
deep, with a capacity of about 200 pounds of water. The 




Fig. 194. — Hoadley's Calorimeter. 

calorimeter was made of three concentric vessels of galvanized 
iron, the spaces being filled with hair-felt and eider-down. 
The condenser consisted of a drum through which passed 
a large number of half-inch copper tubes, the steam being 
on the outside, the water on the inside, of these tubes ; the 
agitator consisting of a propeller-wheel attached to an axis 
that could be rotated by turning the external crank K t effectu- 
ally stirring the water. The thermometer for measuring the 
temperature was inserted in the axis of the agitator at T. 






§ 322,] THE AMOUNT OF MOISTURE IN STEAM. 



409 



In the hands of Mr. Hoadley the instrument gave accurate 
determinations. 

In practice the instrument was arranged as in Fig. 195; the 
calorimeter E was placed on the scales F, and supplied by 
cold water from the elevated barrel A. The temperature of 
the entering water was taken at C. Steam was admitted to 
the condensing-coil until the temperature of the condensing 
water reached, say, 1 io° F. The weights before and after 




k°) (sj- 



Fig. 195. — Hoadley's Calorimeter Arranged for Use. 



adding steam were taken by the scales F; the temperature ot 
the warm condensing water was taken by a thermometer, G t 
inserted in the axis of the agitator. The water-equivalent was 
determined as explained in Article 317, page 401, and the 
quality computed by equation (6), page 394. The rate of 
cooling was determined, and an equivalent amount added as a 
correction for any loss of heat by radiation. 

322» The Kent Calorimeter. — This instrument differs 
from the Hoadley instrument principally in the arrangement of 
the condensing coil. This when filled with steam could be 
removed from the calorimeter, so as to enable the weight ot 



4io 



EXPERIMEN TA L ENGINEERING. 



[§ 323- 



steam to be taken on a smaller and more delicate pair of scales 
than those required for the condensing water, thus giving 
more accurate determinations of the weight of the steam con- 
densed. 

323. The Barrus Continuous Calorimeter. — This calo- 
rimeter is shown in Fig. 196 in section and in Fig. 197 in per- 
spective. It consists of a steam-pipe, a/, surrounded by a 




Condensed Steam 
Fig. 196.— Barrus Continuous Calorimeter. 



tub or bucket, O, into which cold water flows; the condensing 
water is received as it enters the bucket in a small brass tube, 
k, surrounding the pipe a, and is conveyed over and under 
baffle-plates, m, so as to be thoroughly mixed with the water 
in the vessel, and is finally discharged at c. Thermometers are 
placed at /and at g to take the temperature of the water as it 



§ 3 2 3-] THE AMOUNT OF MOISTURE IN STEAM. 



4 II 



enters and leaves, and finally the condensing water is caught 
from the overflow and weighed. The condensed steam falls 
below the calorimeter ; by means of the water-gauge glass at " 




Fig 197 — The Baruus Continuous and Superheating Calorimeters. 

it may be seen and kept at a constant height. The temperature 
of the condensed steam while it is still under pressure is shown 
by a thermometer at h. In order to use the calorimeter it is 
necessary to weigh the condensed steam ; this cannot be done 
without further cooling, as it would be converted into steam 
were the pressure removed. For this purpose it is passed 
through a coil of pipe immersed in a bucket filled with water, 



412 EXPERIMENTAL ENGINEERING. [§ 324. 

shown at 5 in Fig. 197. The water used in the cooling bucket 
5 has no effect on tne quality of the steam and is not con- 
sidered in the results ; it is allowed to waste, but the condensed 
steam is caught at W, Fig. 197, and weighed. 

The quality of steam is computed by omitting k in for- 
mula (6), page 394. Hence 



w r r ' 



w is the weight of condensed steam after correction for radia- 
tion-loss as explained in Article 324 ; w being equal to w' — u. 

324. Directions for Using the Barrus Continuous Calo- 
rimeter. — Apparatus needed. — Thermometers ; pail for receiv- 
ing condensed steam ; tank and scales for the condensing water. 

Directions. — I. Fill the thermometer-cups with cylinder- 
oil. (Do not put thermometers in place until apparatus is 
working.) 

2. Turn on condensing water and steam ; regulate the flow 
of condensing water so as to keep the bucket O nearly full, and 
the temperature of the discharge-water as much above tem- 
perature of the room as injection is below : this should be 
about no° F. Regulate the flow of condensed steam so as to 
keep the water in the glass e at a constant level. Turn water 
on to the cooling coil in the bucket S, and reduce the con- 
densed steam to a temperature of about 120 . 

3. After the apparatus is working under uniform condi- 
tions, put the thermometers in the cups for temperature of 
injection and discharge water, and having previously weighed 
the vessels, at a given signal, note time and commence to 
catch the condensed steam and the condensing water. Con- 
tinue the run until about 360 or 40c pounds of condensing 
water has run into the receiving tank. Without disturbing 
the condition of the apparatus, commence simultaneously to 
waste the discharge from both pipes. Find the weights of 



§ 324.] THE AMOUNT OF MOISTURE IN STEAM. 4 1 3, 

condensed steam (w') and condensing water (W) ; note time of 
ending run. 

4. Make three more runs similar to the first. 

5. To find the radiation-correction of the instrument: 
Empty the bucket of condensing water, and surround the 
condensing tube a with hair-felting ; make a run of the same 
length, and with steam of same pressure as in the previous 
runs. The weight of steam conden-sed will be the radiation- 
loss, which we call u, and is to be deducted from the weight of 
condensed steam obtained in the previous runs of the same 
length. Find the condensation per hour. 

6. Work up quality of steam by the formula 



b^v- '.)-(' -'.)]-*- 



Make report as described for other calorimeters. 

Example. — The following is the result of a trial with the 
Barrus continuous calorimeter: Temperature of injection-water, 
/, = 37°. 5 Fahr. ; temperature of discharge-water, / 2 = 83°.8 
Fahr. ; temperature of condensed steam, t % = 304.9 Fahr. ; 
steam-pressure by gauge, 72.4 lbs. ; temperature of entering 
steam, t = 31 7°. 9 ; length of test, 40 minutes ; weight of cool- 
ing water, W = 573.5 lbs. ; weight of condensed steam, w' = 
29.89 lbs. ; radiation-loss u = 0.13 lb. Neglecting value of u, 

x = 573.5 (83-8 - 37.5) _ (3I7-9-3Q4-9) 
29.89 891 891 

19.21 X 46.3 — 13.0 876.4 
~ 8oTi = I9T - 98 ' 4 * 

x — 98.4 if not corrected for radiation-loss. If corrected, 

*= (^46.3-130)^891 = 98.9. 



414 EXPERIMENTAL ENGINEERING. [§ 325. 

325. Forms for Use with Condensing Calorimeters. 

MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL 
UNIVERSITY. 

Priming Test with Condensing Calorimeter. 



Made 07. 
Tsst cf . , , . 



Kind of calorimeter 



189.. 



Steam. 



N. Y. 







I. 


II. 


III. 


IV. 


V 








Duration of run , minutes 


Symbols. 




























P 

V 

W-i- V 












Scale-readings, tare, lbs 

Tare and cold water, lbs 


































Quantities : 


w 

w 
h 

?2 
h 

t 

W -7- w 

X 
I — X 

D 
























Temperatures, deg. Fahr. : 

Condensing water, cold 

Condensing water, warm 
































Steam at pressure P 














































Degree of super-heat 























Correction due to displacement of water by hose lbs. 

Calorimeter-equivalent lbs. How found 



Temp, r^ cm deg. Fahr. Barometer-reading inches. 

W 1 



Quality x = j — (/a — ti 



Degree of super-heat D = (x — i)r -5- 0.48. 



§ 325-] THE AMOUNT OF MOISTURE IN STEAM. 
CALORIMETER TEST. 
Date No 



415 



No. of 


a 


u 

c 
u 

s 


Condensing 
Water. 


Condensed 
Water. 


Temperature of 

Condensing 

Water. 


h «j -v. 

3 en 

5 <u u 

ill 


I s ' 

io 

H 


to 
to 

V 

a 

D . 




1* 



Signal. 


Weight. 


Diff. 


Weight. 


Diff. 

w 


Hot. 


Cold. 
h 


s 




























Total . 


























Aver.. 


























Cor. . . 





















































Duration of test min. 

Weight of steam condensed lbs. 

Weight of condensing water „ . *' 

Average temperature of hot condensing water C; ... .Fahr.; . . . .B.T.U. 

«« it <( qq\A << <« «« <« «« 

" " " condensed steam " .... " .... " 

" " "room " ....deg. C. 

" pressure of air lbs. per sq. in. 

" absolute pressure of the steam ..<>.... " " " 

Thermal units in water corresponding to absolute pressure of steam.. . .B.T.U. 

Heat acquired by condensing water " 

Heat given up by condensed steam in cooling to temperature of ther- 
mometer in same. , " 

Weight of water condensed by radiation lbs 

Heat given up by each pound of steam in condensing... B.T.U. 

Latent heat of one pound of steam at average absolute pressure " 

Per cent of • , 

Signed 



416 



EXPERIMENTAL ENGINEERING. 



[§ 326, 



STEAM TO BE TESTED"- 



326. Barrus Superheating Calorimeters. — In the Barrus 
Superheating Calorimeter, Fig. 198, the steam-pipe leading from 
the main is bifurcated, one branch, E y 
passing over the flames of a large 
Bunsen burner, the other passing up- 
ward, and finally downward, when it 
is jacketed by the enlargement of the 



■STEAM FOR SUPERHEATER 





DCIH 



temp 



first branch. The branches discharge 
separately, each through equal orifices, 
about one-eighth inch in diameter. 

This instrument is shown in Fig. 198 
in elevation, and on the left-hand side of 
Fig, 197 in perspective. The steam in 
one branch is superheated at G\ that in 
its normal condition is received at H, and 
is discharged at N. The superheated 
steam forms a jacket from I to K outside 
the sample to be tested, and is discharged 
at the orifice M. The temperature of the 
jacket steam is taken at A and at B ; that 
of the normal steam is measured at C, as 
it is discharged ; it is found as it enters from its pressure taken 
at H, by reference to the steam-table. 

The theory of this calorimeter is as follows: 




—Barrus Super- 
heating Calorimeter. 



§ 326.] THE AMOUNT OF MOISTURE IN STEAM. 417 

1. An equal weight of steam flows through each branch of 
the pipe. 

2. The steam, superheated by the gas-flame, is used as a 
jacket for the other branch, and parts with as much heat, ex- 
cept for radiation, as the other gains. 

3. This amount may be measured provided the steam dis- 
charged from the central tube is superheated. 

To measure this gain or loss of heat, thermometers are 
placed to take the temperature of steam as it enters and leaves 
the jacket, and on the central pipe near the same places. 

Formula. — Let (1 — x) be the amount of water to be evap- 
orated ; in so doing it will take up from the jacket-steam 
r(i — x) heat-units. Let t be the normal temperature of the 
steam at the gauge pressure ; let T x be the temperature of the 
superheated jacket-steam at entering, and T 9 as it leaves ; let 
T 3 be the temperature of the superheated steam discharged 
from the sample pipe, and let radiation-loss in degrees F. be 
/. If the specific heat of steam be 0.48, since gain and loss of 
heat are equal, we have 

0.48(7; - 7, - /) = r(i - x) + 0.48(7-3 - t). 
.-. i-* = o.48[r,- T,-/-(T 3 -l)-] + r; 

from which x may be found. 

To find /, the radiation-loss in degrees, shut off steam in 
the branch leading to the centre steam-pipe, and find reading 
of thermometers T x and 71, . After a run of same length as in 
test, take ■/= T x — T % . 

Directions for using Barrus Superheating Calorimeter. — Ap- 
paratus needed. — Three thermometers reading 400° F. each, 
and pressure-gauge, superheating lamps, etc. 

First. Calibrate instruments, and ascertain by a run of 
twenty minutes that equal amounts of steam are discharged 
from each orifice. This may be done by condensing the steam. 

Second. Put cylinder-oil in oil-cups ; attach gauge. 






41 S 



EXPERIMENTAL ENGINEERING. 



[§ 328. 



Third. Put in working order ; after thermometer at end of 
sample-steam-pipe shows superheat, commence the run. 

Fourth. Take readings once in two minutes for twenty 
minutes. 

Fifth. Obtain radiation-loss / as explained. 

Sixth. Work up results as explained, and make report as 
in previous cases. 

327. Form for Determination with Barrus Superheat- 
ing Calorimeter. 



No. 



BARRUS SUPERHEATING CALORIMETER. 
Date 



Time. 


Temp. 

Jacket-steam 

Entering. 


Temp. 

Jacket steam 

at Exit. 


Temp. 

Sample Steam 

at Exil. 


Steam- 
pressure by- 
Gauge. 


Barometer. 














Total 












Average . . 












Corrected. 

























Duration of test min. 

Barometer in. ; lbs. per sq. in. 

Sample steam, gauge pressure lbs. per sq. in. 

" " absolute " lbs. per sq. in. 

'* " temperature at absolute pressure C; F. 

"outlet C; F. 

Superheated steam, temperature at inlet C. ; F. 

" * 4 " "outlet C; F. 

Latent heat of steam at absolute pressure B. T. U. 

Specific heat of superheated steam B. T. U, 

Correction for condensation 

" " radiation „ 

Per cent of moisture in steam 



328. The Throttling Calorimeter. — This instrument was 
designed in 1888 by Prof. C. H. Peabody of Boston, and rep- 



§ 328.] THE AMOUNT OF MOISTURE IN STEAM. 



419 



resents a greater advance than any previously made in practical 
calorimetry. The equations for its use and limitations of the 
same were given by Prof. Peabody in Vol. IX., Transactions 
Am. Society Mechanical Engineers. As designed originally, 
it consisted of a small vessel four inches in diameter by six to 
eight inches long, and connected 
to the steam-supply with a pipe 
Containing a valve, &, used to 
throttle the steam supplied the 
calorimeter. Fig. 199 shows the 
original form of the calorimeter, 
which is arranged so that any de- 
sired pressure less than that in the 
main steam-pipe can be maintained 
in the calorimeter A. The press- 
ure in the calorimeter is shown by 
a steam-gauge at g, and the tem- 
perature 'by a thermometer at D\ 
the main steam-pipe is provided 
with a drip at f, to drain the pipe 
before making calorimetric tests. 
In using the calorimeter, any desired pressure can be main- 
tained in the vessel A by regulating the opening of the ad- 
mission and exhaust valves. 

The effect of this operation will be to admit the heat due 
to high-pressure steam into a vessel filled with steam of lower 
pressure. The excess of heat is utilized firstly in evaporating 
moisture in the original steam ; secondly, if there is sufficient 
heat remaining, in raising the temperature in the vessel A 
above that due to its pressure, thus superheating the steam. 
Unless the steam in the chamber A is superheated, no deter- 
minations can be made with the instrument. The equation for 
its use is obtained as follows : the heat in one pound of high- 
pressure steam before reaching the calorimeter is expressed 
as in formula (2), Article 311, page 393, by xr -f- q. After 
reaching the calorimeter the heat is that due to the press- 




Fig. 199.— Peabody's Throttling 
Calorimeter. 



420 



EXPERIMENTAL ENGINEERING. 



[§ 32S. 



ure in the calorimeter added to that due to the superheat, or 
A, -|-o.48( T t — 7^). Since these quantities are equal, 



xr + g = \, + o.48(T l -T c ); 



from which 



x = lK-q + o.4&{T t - T c )1 + r 



00 



in which r equals latent heat, and q heat of liquid due to 
pressure in main pipe as given in the steam-table. 

X c = total heat in one pound of dry steam at calorimeter 
pressure ; T x = reading of thermometer in calorimeter, and 
T c = normal temperature of steam in calorimeter due to calo- 
rimeter pressure. Care must be taken that both X c and q are 
given in the same units. 

Example, — Suppose that the gauge pressure on the main 
steam-pipe is 80 pounds, that on the calorimeter 8 pounds 
atmospheric pressure 14 pounds, as reduced from the barom- 
eter-reading, and that the thermometer in the calorimeter 
reads 274°.2 F. Required the quality of the steam. 

In this case we obtain the following quantities from the 
steam-table : 



Entering steam. 
In calorimeter. . 



p 

Absolute 
Pressure. 


T 

Temperature 

Deg. F. 


q 

Heat of 
Liquid, 
B. T. U. 


X 

Total 

Heat, 

B. T. U. 


94 
22 


323-1 
233-1 


293.2 
202.0 


"53-o 



r 

Latent 

Heat. 

B. T. U. 



887.3 
951.O 



From which 



* = [1 153 - 293-2 + 0.48(274.2 - 233.1)] -r- 887.3 ; 
^ = 99.1. 



Per cent of moisture, 100 — x — 0.9. 



§ 3 2 9-J THE AMOUNT OF MOISTURE IN STEAM. 42 L 

329. Recent Forms of Throttling Calorimeters These 

instruments differ from Peabody's principally in size and 
form. They all work in the same general manner and 
detailed descriptions are hardly necessary. 




Fig. 900.— Heisler's Throttling Calorimeter. 

Heisler's throttling calorimeter is shown in Fig. 200, 
with attached manometer for measuring the pressure in the 
calorimeter chamber, it is of small size and keeps the current 
of steam intimately in contact with the thermometer. 

Carpenter's throttling calorimeter, shown in Fig. 201, is pro- 
vided with an attached nozzle for spraying the sample of 
steam over the themometer-bulb. The instrument may be 
used with or without a thermometer-cup, but in every case 
the thermometer must be deeply immersed in the steam. 
This instrument is made by SchafTer and Budenberg, New York. 



422 



EXPERIMENTAL ENGINEERING, 



[§330 



TO MANOMETTB 




Fig. 201.— Carpenter's Calorimeter. 



Throttling Calorimeter of Pipe-fittings. — A very sat- 
isfactory calorimeter can be made of pipe-fittings, as shown 




: B 



Fig. 202.— Throttling Calorimeter of Pipe-fittings. 
in Fig. 202. Connection is made to the main steam-pipe, 
as explained already elsewhere. The calorimeter is made 



THE AMOUNT OF MOISTURE IN STEAM. 



423 



§330 

of f inch fittings arranged as shown ; the steam-pipe W is of 
|-inch pipe, and the throttling orifice is made by screwing on a 
cap, in which is drilled a hole -J or T V inch in diameter. 

A thermometer-cup, Fig. 190, page 400, is screwed into the 
top, and an air-cock inserted opposite the supply of steam. A 
manometer, B, for measuring the pressure is attached by a 
piece of rubber tubing as shown. The exhaust steam is dis= 
charged at E. The back-pressure on the calorimeter can be 
increased any desired amount by a valve on the exhaust-pipe ; 
when no valve is used the pressure is so nearly atmospheric 
that a manometer is seldom required. 

Method of finding Normal Temperature in the Calor- 
imeter. — It is essential to know the normal temperature 
within the calorimeter; this will vary with the pressure on the 
calorimeter, which pressure is equal to the barometer-reading 
plus the manometer-reading. 

The following table gives the normal temperature corre- 

TABLE OF BOILING-POINTS. 



Normal 


Total Pressure 


Normal 


Total Pressure 


Temperature. 


on Calorimeter. 


Temperature. 


on Calorimeter. 


Degrees F. 


Inches Hg. 


Degrees F. 


Inches Hg. 


209.5 


28.466 


• 7 


•744 


.6 


•523 


.8 


.803 


•7 


.580 


•9 


.863 


.8 


.037 


212.0 


.922 


•9 


.095 


.1 


.982 


210.0 


.752 


.2 


30.041 


.1 


.8lO 


•3 


.101 


.2 


.867 


• 4 


.I6l 


•3 


.925 


•5 


.221 


•4 


•983 


.6 


.281 


•5 


29.O4I 


•7 


•341 


.6 


.099 


.8 


.401 


•7 


.157 


•9 


.462 


.8 


.215 


213.0 


.522 


, -9 


.274 


.8 


31.004 


211. 


•332 


214.0 


.107 


.1 


•391 


215.0 


.692 


.2 


•449 


216.0 


32.277 


•3 


.508 


217.0 


.862 


•4 


.567 


218.0 


33-447 


•5 


' .626 


219.0 


34.032 


.6 


.685 


220.0 


.617 



Difference i° F =- 0.585 inch. Difference 1 inch = l .709. 






424 EXPERIMENTAL ENGINEERING. [§332 

sponding to various absolute pressures nearly atmospheric, ex- 
pressed in inches of mercury: 

In the use of the instrument the total pressure in the 
calorimeter is to be taken as the sum of the barometer-reading 
and the attached manometer. The degree of superheat of the 
steam in the calorimeter is the difference between the tempera- 
ture as shown by the pressure and that shown by the inserted 
thermometer. 

Graphical Solution for Throttling-Calorimeter Deter- 
minations. — In the practical use of this instrument it is 
customary to exhaust at atmospheric pressure, so that the 
normal temperature in the calorimeter is the boiling-point at 
atmospheric pressure, and X c is 1 146.6; in which case formula 
(11) becomes 

1 146.6 + 0.48(7; — 212) ■— q 

x = ' 

r 

1 146.6 — q , 0.48(7, — 212) 



If in this form we suppose the steam-pressure constant, and 

the degree of superheat and quality of steam alone to vary, 

r and q will both be constant, and we shall have the equation 

1 146.6 — q . 
of a right line, in which is the distance above the 

origin that the line cuts the axis of ordinates, and 0.48 -=- r is 
the tangent of the angle that the line makes with the axis of 
abscissae. Drawing lines corresponding to the different gauge 
or absolute pressures, a chart may be formed from which the 
values of x may be obtained without calculation. 

Using degrees of superheat in the calorimeter as abscissae 
and absolute steam-pressure as ordinates, and drawing lines 
corresponding to various percentages of moisture, we have a 
diagram shown in Fig. 203, from which the results of observa- 
tions made with the throttling calorimeter may be taken at 
once without further calculation. 



'fti 


-M 


_ fl 


§'- 


»l: 




^i## :; #t|ttf 


H E iP"-i 




"Wffr : 


^TFT 




1 1 j [ |/| 1 1 j j 


- f i *■+- 


1 TTT f ! Tt/l 

1 j 1 7TT1 1 1 1 ; Hi!' 1/T 




-Ue 


: a | j 1 1 cgE 

"Til" 
r" / - 


f-4444 




m 11 Ml 


"1 nti" 
lljlll -||| 


-H-hiFTp /""Tntl 7TT 
|JJB:S| 


i 1 i Fi il i J--rT^- 

jtrtTttp] 

±Jl||Hx): | [ r j , l 


11 

y 

■*jj 

§1 
§g 

5e 


T^Trr 

\y'\ 

9J-H-H- 

ill 

si 


1 


-\v_: 


Ififfi 


IT 1/ 

-U-H- :: 

+141°^ 
- - 


Lj 1 h 1 ^ 

I/Im rfiT 


WJ\ j 1 j 1 = 4r : 

1 ' ! TKjTTj 
I i'l | i If 

1 V\ 1 j H-^ 

MJ-JJ+-/-- 


1 1T IT !"'" ' /ill ' / 

I | i 4+ H -j+r -- TTTTTM 

1 ' /[ lh { ' 

IpM 111 !>ffi 

I'll _LV/ 1 1 1 1 1 /WW 

TiliU'r+^ij i p i : 


P-LLj- jc -i-j-t- — i 

*1 j 1 j ' j -fffi 4ffl : 


i 


^~T- 

S3 


1 


I 


||Jm 


4M 

II 


ttw- 

11 

j \y 
ffrflf 


wfcpff 
jljlljl 


1 1 i/i i 

"tttttt"""^! 

iM' :: 

W 1 riir 


■tA in- = R" ^ -j-j f- -Fl 4-T- -1 Wr 

^ ffl^ frftt 4 S Ttft 

JT " T ^ Tl 175^ TNT 
"I 7 ITT iffi'TII TRT 

1:1 llll 

ffiiiiiiBiB 

:|jl|J|; M ;: 

:T:H:ROf^L±N:G: iC:K.£f 


r "m — n~tj 

lillllllil/; 11 !'! 

ffff 
Irj j I; ; " 

t : "| 1 i l»r 

T — rril | ' 1 ' : 
1 ] 1 1 i 

JlRtMEfTERt: 


Wr 


















j 1 1 1 1 1 | ' 1 "--- + -J-4--""- 


|;;;:;S:ffi 


ffl 


....J- 






tH-H- 


~S±Ea 

d^-rIe 
--T-I-+H 


-'it Eh. 

E-S4G- 


4w- 


©WheWc:: 
r-h e"act- 1 n- -t-4 

mm 


I'RE'SStlF'-'- +^ 

Sl:|:±:::::|:::::::: 

H-EfG-A-bO R 1- \fl-E-T E-R 





Fig. 203.— Diagram giving Results from Throttling Calorimeter 
without Computation. 






426 EXPERIMENTAL ENGINEERING. [§333 

Use of the Diagram. — To find the percentage of moisture in 
the steam from the diagram, pass in a horizontal direction along 
the base-line until you arrive at the number corresponding to 
the degree of superheat in the calorimeter; then pass in a ver- 
tical direction until you reach the required absolute pressure 
of steam. The position with reference to the curved lines 
shows at once the percentage of moisture, and can be read 
easily to one tenth of one per cent. Thus, for example, sup. 
pose that we have the following readings : Barometer, 29.8 
inches; attached manometer, 1.5 inches — making a total press- 
ure in the calorimeter of 31.3 inches, corresponding to a tem- 
perature of 2I4°.27 Fahr. Steam-gauge, 80 pounds; absolute 
pressure, 94.7 pounds; thermometer-reading in calorimeter, 
254 Fahr. From which the degree of superheat is found to 
be 254 -2i4°.27=r39 .73. 

Following the directions as given, the percentage of moist- 
ure is seen from the diagram to be 1.66 per cent. The quality 
would be 1.00 — 1.66 = 98.34 per cent. While the diagram is 
especially computed for determinations when the pressure in 
the calorimeter is atmospheric or but slightly above, it will be 
found to give quite accurate results when the calorimeter is 
under pressure, by considering that the ordinates represent the 
difference of pressures on the steam and in the calorimeter. 
Thus, in the example, Article 328, page 390, the steam-pressure 
was 80 pounds, calorimeter-pressure 8 pounds ; degree of super- 
heat 274.2 — 233.I = 41. 1 ; resulting quality by calculation 99.1, 
indicating 0.9 per cent of moisture. Using difference of press- 
ure 80 — 8 = 72 as ordinate, and 41. 1 as abscissa, we find from 
the chart that the percentage of moisture is 0.92 ; from which 
x — 99.08. 

The results for the throttling calorimeter may be com- 
puted from the temperatures instead of the pressure of the 
original sample of steam as compared with the temperature 
in the calorimeter when at atmospheric pressure. Carpenter's 
calorimeter, Fig. 201, is especially adapted for such determina- 
tions, since it provides an easy method of calibrating the 
thermometer when in position. This is especially important 
since thermometers will ordinarily read two or three degrees 
low when there is a portion of the stem exposed. 



§ 333-] THE AMOUNT OF MOISTURE IN STEAM. 427 

For using the instrument in this manner, the boiling- 
point in the calorimeter is first determined by opening both 
the supply and discharge valves C and D and showering the 
instrument and connections with water until the steam in the 
calorimeter is' moist, in which case the reading of the ther- 
mometer will be that due to the boiling-point. Second, close 
the discharge-valve with the supply- valve open and obtain 
full boiler pressure in the calorimeter; when the thermometer 
has become stationary note the temperature: this will be the 
boiling-temperature for the given pressure as read by the 
given thermometer. Third, open the discharge-valve of the 
instrument, and after the mercury has become stationary note 
the reading of the thermometer. Deduct from this latter 
reading the reading first taken and we shall have the degree 
of superheat in the calorimeter. From these two numbers 
the quality may be computed by reference to steam tables as 
explained, but it is more easily done by reference to the 
following diagram, in which the temperature of the steam is 
the ordinate and is that given when the discharge-valve is 
closed, and the temperature in the calorimeter is the abscissa, 
on the supposition that the boiling-temperature at calorimeter 
pressure is 212 degrees. If the boiling-temperature is more or 
less than this amount, a corresponding correction must be 
made to the result. As an illustration, suppose that the 
boiling-temperature in the calorimeter is 2 1 1 or one degree 
low, that the actual temperature in the calorimeter when both 
valves are open is 265, and that the temperature of the steam 
obtained with the discharge-valve closed is 320. To find the 
quality we look in the line over 266 and opposite 330, and 
read the results by the diagonal lines, the quality as shown 
on the diagram being 98.8 (see Fig. 204). 

Limits of the Throttling Calorimeter. — To deter- 
mine the amount of moisture that can be evaporated by 
throttling, make T x = T c in formula (11) ; then 

x = (A,— -q) ~-r (12) 

The amount of moisture that can be determined by the 



TEMPERATURE IN CALORIMETER 
220 230 £40 250 260 270 £80 290 300 310 320 330 340 




•fer ~'^y ! - -; i=v:-|.:^i i.vfeoo^-276=^soEt' r m-^r= w=\^m 



- TEMPERATURE IN CALORIMETER 
Fig. 204.— Diagram for Computing Results with Throttling Calorimeter. 



§3551 



THE AMOUNT OF MOISTURE IN STEAM. 



429 



throttling calorimeter in expanding from the given pressure 
to atmospheric, as computed by substituting in formula (12), 
is as follows : 

LIMITS OF THE THROTTLING CALORIMETER. 



Pressure, pounds per square in. 


Maximum per 
cent of prim- 
ing. 


Quality of the 
steam, per cent. 


Absolute. 


Gauge. 


300 
250 
200 
175 
I50 
125 
100 

75 
50 


285.3 
235-3 
185.3 
160.3 
135.3 

no. 3 

85.3 . 
60.3 

35-3 


07. 7 
7-0 
6.1 
5.3 
5.2 
4.6 
4.0 
3-2 
2-3 


9 2 -3 
93-o 
93-9 
94.2 
94.8 

95-4 
96.0 
96.8 
97-7 



By reducing the pressure below the atmosphere, the limits 
of the instrument may be somewhat increased. 

Directions for Use of Throttling Calorimeter. — 

Apparatus. — Steam-thermometer; pressure-gauge; manometer 
for measuring pressure in calorimeter in inches of mercury. 

1. Attach the calorimeter to a perforated pipe extending 
well into the main steam-pipe to secure a fair sample of steam. 
Calibrate all the apparatus. 

2. Fill thermometer-cup with cylinder-oil, having first care- 
fully removed any moisture from the cup. Place thermometer 
in the cup, and after it has reached its maximum commence 
to take observations. 

3. Read steam-pressure, attached manometer, and tempera- 
ture at frequent intervals. 

4. Compute the quality of the steam for each observation. 
Forms for Throttling-Calorimeter Determinations. 



Priming tests of. 
Made by 



189. . . . 



at ., N. Y., 

with Throttling Calorimeter. 

Steam used during run Ibs^ 



Barometer-reading , . .inches. 



430 



EXPERIMENTAL ENGINEERING, 



[§336 











1 


2 


3 


4 


5 


6 


7 


8 


9 






3 


v> 1 




m 

t x 

tc 

P 

o.&it-t') 
Kc 

r 

Kc — q 

1 — X 

X 

D 


Time 














1 


Steam-pressure, main 




















00 


Manometer reading calo- 




















-f 


Observed temperature 




















Heat at steam-pressure P. 
Normal temperature in 




















< 




















11 


Absolute pressure in 




















a 1 

% s. 






















Total heat, pressure m... 

Latent heat for pressure 

P 








v- 3 












uality 
egrees s 


Ac— y + o.48(/,— tc) 

Per cent of entrained 
water 








































a a 















































AVERAGE RESULTS OF CALORIMETER TEST. 

Date 

Duration of test. > min. 

Barometer in. ; . . lbs. per sq. in. 

Boiler-pressure by gauge " 

" absolute " " 

Calorimeter-pressure by gauge " •' 

absolute " " 

Calorimeter-temperature *. C; F. 

Per cent of moisture in steam 

Signed 

336. The Separating- Calorimeter. — The separating 
calorimeter is an instrument which removes all water from 
the sample of steam by some process of mechanical separa- 
tion, and provides a method of determining the amount of 
water so removed and also the weight of the sample. This 
process is dependent upon the greater density of water as 
compared with that of steam. Thus, for instance, steam at 
100 lbs. absolute pressure is more than 260 times lighter than 
water at the same temperature, and if the sample of steam 
when moving with considerable velocity can be made to 
change its direction of motion abruptly, the water will be 
deposited by the action of inertia. 



§ 33 6 -] 



THE AMOUNT OF MOISTURE IN STEAM. 



431 



The accuracy of this instrument depends on the possibility 
of completely separating the water from the steam by 
mechanical methods. To determine this a series of tests 
were conducted for the author by Messrs. Brill and Meeker 
with steam of varying degrees of quality. The range in 
moisture was from 33 to 1 per cent, yet in every case the 
throttling calorimeter attached to the exhaust gave dry steam 
within limits of error of observation. The following were the 
results of this examination. 

SEPARATING CALORIMETER. 













Examination of Exhaust 




Observations on Entering Steam. 




Steam from Calorimeter by 












Throttling- Calorimeter. 




T 


P 


w 


w 


X 


t 


X 


No. of 
Obser- 
vations 


Calori- 
meter. 


Duration 
Run, 


Gauge 
Pressure, 


Pounds 

Separated 

Water in 

Run. 


Pounds 

Condensed 

Steam in 

Run. 


Quality 
Steam, 


Temp, in 
Calori- 


Quality 
Steam in 




minutes. 


pounds. 


per cent. 


meter. 


Exhaust. 




i\ 


25 


81.5 


I-I5 


4.45 


79.46 


281 


99-95 


6 


25 


78.2 


O.15 


5.20 


97.2 


281.3 


IOO.OO 


6 


i\ 


25 


80.8 


0.525 


4.25 


89.005 


286.5 


IOO.OO 


6 


25 


79-5 


O.150 


4-75 


96.94 


281.8 


99-95 


6 


i\ 


25 


78.5 


O.300 


5.000 


94-34 


2S2.8 


100.00 


6 


25 


77.6 


.150 


5-45 


97-32 


282.3 


100.00 


6 


i\ 


24 


79-5 


1.8 


4-55 


71.65 


280.I 


99.94 


6 


24 


78.5 


1.4 


4.90 


77-77 


279-5 


99.9 


6 


i\ 


20 


83.5 


1. 15 


4.1 


77.67 


286.5 


100.00 


5 


20 


81.6 


1.70 


4-75 


73-64 


282.7 


99.98 


5 




20 


74.8 


0.65 


3-95 


85.87 . 


283.7 


100.05 


5 




20 


82.0 


0.85 


3-95 


82.29 


286.8 


100.05 


5 




20 • 


82.6 


o.35 


4-15 


92.22 


285.6 


100. 


5 




20 


81.5 


0.20 


3-95 


95-15 


285.2 


100.05 


5 


1! 


20 


81.4 


2.20 


4 • 325 


66.28 


283.1 


100. 


5 


20 


80.3 


0.30 


4-55 


93.81 


282.8 


100. 


5 


i\ 


20 


82.0 


0.20 


4-65 


95-8 


282.8 


99.98 


5 


20 


81. 1 


0.20 


4.40 


95-7 


284.0 


100. 


5 


Averaj 


r e of 18 trials, invr 


)lving 98 


observati 


oris 




99.998 















This experiment indicates that the complete separation of 
moisture from steam is possible by mechanial means. 

Any radiation in the instrument will increase tne apparent 
moisture in the steam, and must also receive consideration, 
especially if it be sufficient in amount to sensibly affect the 
results. 



432 



EXPERIMEN TA L ENGINE ERING. 



[§ 337- 



337. Description of Various Forms. — The earliest form 
of separating calorimeter used in experimental work, in the 
Sibley College laboratory, consisted of a vessel with an interior 



G n 




Fig. 205. — The Separator Calorimeter. 
oozzle, extending below the outlet and so arranged that the 
eurrent of steam would abruptly change direction and deposit 
the moisture into the bottom portion of the vessel. The dry 
steam was allowed to escape near the top. Fig. 205 shows 



§ 337-] THE AMOUNT OF MOISTURE IN STEAM. 433 

a form, used in the early experiments, which was constructed 
of pipe-fittings. 

This instrument, even when covered with hair felt, gave 
off sufficient amount of heat to sensibly affect the results, and 
a correction for radiation was essential. The amount of radia- 
tion was determined by using two instruments of the same 
kind and size, arranged so that the discharge from one was 
the supply to the other. 

The second instrument receives perfectly dry steam from 
the first, the water deposited is due to the radiation loss, 
which, being the same in both instruments, provides a method 
of determining its amount. In figuring the percentage of 
moisture, the amount thrown down by radiation in the second 
instrument is to be deducted from the total amount caught 
in the first calorimeter. 

In later forms of the instrument the amount of radiating 
surface has been made so small as to render the correction for 
radiation, in all ordinary cases, negligible, by constructing 
the instrument in such a manner as to be jacketed by steam 
of the same pressure and temperature as in the sample. The 
form of this instrument is shown in Fig. 207, in which the 
steam is supplied through the pipe D, the moisture being 
received in the interior vessel E, the discharge steam passing 
out of the chamber E at the top, into the jacket F, and thence 
out of the instrument through a small opening at L; the 
opening at L being made sufficiently small to maintain the 
pressure in the jacket the same as that in the sample. The 
discharged steam is then condensed in a can, J. This can is 
provided with a small top in which is set a gauge-glass with 
attached scale, graduated so as to read to pounds and tenths 
of pounds of water. A gauge-glass N attached to the 
calorimeter is provided with index, inn, arranged to move 
over a graduated scale, S, which shows the weight of water in 
the vessel E in pounds and hundredths. In using this 
instrument the condensing can J is filled with water to the 
zero-point of the scale. The amount of condensed steam is 



434 EXPERIMENTAL ENGINEERING. [§ 337- 

read on the scale of the can, J\ the amount of water in the 
sample of steam for the same time is read on the scale 5. 
The percentage of moisture, in case radiation is neglected, is 
the quotient of the reading of the calorimeter scale 5 
divided by the sum of the readings on both scales. 

The latest form of the instrument is shown complete with 
all accessories in Fig. 206, and is a great improvement over 
the earlier forms in points of portability and convenience. It 
differs principally from the form last described in the con- 
struction of the steam-separating device, which has been 
increased in efficiency and in the substitution of a gauge 
attached to the outer jacket, which registers the total flow of 
steam through the instrument in ten minutes of time. 

The flow of steam through a given orifice is proportional 
to the absolute steam-pressure, by Napier's law* which has 
been proved correct for pressures above 25 pounds absolute; 
and hence it is possible to calibrate by trial a pressure-gauge 
in such a manner that the graduations will show the flow of 
steam in a given time. The only error which is produced in 
this graduation is that due to changes in barometric pressure, 
which is never sufficient to sensibly affect the results obtained 
in the use of the instrument. Should any doubt arise, the 
accuracy of the readings of the gauge are easily verified by 
condensing the discharged steam for a given period of time. 
This should be done occasionally to test the gaduations. 

The instrument may be described as follows: It consists 
of two vessels, one being interior to the other; the outer 
vessel surrounds the interior one so as to leave a space which 
answers for a steam-jacket. The interior vessel is provided 
with a water-gauge glass 10 and a graduated scale 12. The 
sample of steam whose quality is to be determined is supplied 
through the pipe 6 into the upper portion of the interior 
vessel. The water in the steam is thrown downward into 



* See Transactions American Society Mechanical Engineers, Vol. XL, 
1887, paper by Prof. C. H. Peabody. 



§ 337-] 



THE AMOUNT OF MOISTURE IN STEAM. 



435 



the cup 14, together with more or less of the steam; the 
course of the steam and water is then changed through an 
angle of nearly 180 degrees, which 
causes the entire amount of water to 
be thrown outward through the meshes 
in the cup into the space 3, which con- 
stitutes the inner chamber. The cup 
serves to prevent the current of steam 
from taking up any moisture which has 
already been thrown out by the force 
of inertia. The meshes or fins project 
upward into the inside of the cup, so 
that any water intercepted will drip into 
the chamber 3. The steam then passes 
upward, and enters the top of the out- 
side chamber. It is discharged from 
the bottom of the outside chamber 
through an orifice 8 of known area, 
which is much smaller than any section 
of the passages through the calorimeter, 
so that the steam in the outer chamber 
suffers no sensible reduction in pressure. The pressure in 
the outer chamber, being the same as in the interior, has 
the same temperature, and consequently no loss by radia- 
tion can take place from the interior chamber except that 
which takes place from the exposed surface of the gauge- 
glass and fittings. The pressure in the outer chamber, and 
also the flow of steam in a given time, is shown by suitably 
engraved scales on the attached gauge. The scale for show- 
ing the flow of steam is the outer one on the gauge, and is 
graduated by trial, and gives the discharge of steam in pounds 
in ten minutes of time. The readings on the scale 12 show 
the weight of water in the interior vessel 3, and should be taken 
at the beginning and end of the interval. 

The total size of the instrument is about 12 X 2J inches, 
and its weight about 8 pounds. 




Fig. 206. — Improved Sepa- 
rating Calorimeter. 



436 



EXPERIMENTAL ENGINEERING. 



[§338* 




FlG. 207. — Separating Calorimeter with Condensing Can. 



338. Formula for Use of the Separating Calorimeter, 

— Let w equal the weight of dry steam discharged at the 
exhaust-orifice, W the water drawn from the separator, R the 
water thrown down during the run by radiation. Then the 
quality of the steam is 

w + R 



x = 



W+w' 



the amount of moisture 



w 



I — ■ X 



R 



W + w 



§ 339-] THE AMOUNT OF MOISTURE IN STEAM. 437 

To reduce the radiation loss as much as possible the in- 
strument should be thoroughly covered with hair felt to the 
thickness of 1/2 to 3/4 inch. In this case the total loss by 
radiation will be about 0.4 B. T. U.* per square foot per hour 
for each degree difference of temperature between the steam 
and the surrounding air. This will amount to about 220 
B. T. U. per square foot per hour, or about 1/5 of a pound 
of steam under usual conditions of pressure and temperature. 
In the instrument described the actual exposed surface 
amounts to about 1/12 sq. ft., so that the condensation loss 
may be considered as from 1/50 to 1/60 of a pound of steam 
per hour. The total flow of steam through the instrument 
usually varies from 40 to 60 lbs. of steam per hour, so that if 
the instrument is covered, the radiation loss would be less 
than 1/20 of one per cent. If the instrument be not covered, 
the loss would be about five times this amount, or under usual 
conditions about 1/5 of one per cent. 

The radiation loss can in every case be determined by 
using steam of known quality as determined by the throttling 
calorimeter, or better still by arranging two separating calori- 
meters of exactly the same size in series so that the steam 
exhausted from the first is used as a supply to the second in 
a manner already explained. 

The Limits of the Instrument. — The instrument will give 
correct determinations with any amount of moisture that the 
sample of steam may contain. With steam containing a very 
small amount of moisture, the radiation loss will have more 
effect than with steam containing a great amount. When the 
fact is considered, however, that a sample of steam cannot 
probably be obtained but what differs more than 1/2 per cent 
from the average, the futility of making this correction 
becomes at once apparent. 

339. General Method of Using. — The general method of 
using is given only for the latest instrument described, which 

*See numerous experiments, Carpenter's Heating and Ventilation 
<N. Y., J. Wiley & Sons), Chapter IV. 



43$ EXPERIMENTAL ENGINEERING. [§ 340. 

is briefly as follows: First, attach the instrument to a pipe 
leading to the main steam-pipe as already explained, and so 
as to obtain the fairest sample of steam. 

Second, wrap the instrument and connections thoroughly 
with hair felt, to prevent loss of heat by radiation, leaving only 
the scales visible. 

Third, permit the steam to blow through the instrument 
until it is thoroughly heated, before making any determina- 
tions. 

Fourth, take the initial and final readings on the scale ' 1 2 
at beginning and end* of a* period of ten minutes of time and 
note the average position of the hand on the gauge-dial during 
this time. The pressure should be kept as nearly constant 
as possible during the period of discharge, in which case this 
hand will remain constant. 

Fifth, compute the percentage of moisture as explained by 
dividing the reading on the scale 12 by the sum of the read- 
ings on scale 12 and the gauge-dial. 

Attention is again called to the difficulty of obtaining an 
average sample of steam for the calorimetric determination. The 
principal cause of this difficulty is due to the great difference in 
specific gravity of water and steam, as, for example, at a pressure 
of 100 pounds absolute per square inch a cubic foot of steam 
weighs 0.23 pound; a cubic foot of water at the corresponding 
temperature weighs about 56 pounds, or more than 225 times 
as much. If any great amount of water is contained in the 
steam, it is likely, if moving in a horizontal pipe , to be concen- 
trated on the bottom; if moving downward in a vertical pipe, 
to fall under the influence of gravity and inertia; if moving upward 
in a vertical pipe, it tends to remain at the bottom until absorbed 
or taken up by the current of steam. The amount of water by 
weight that will be absorbed as a mist or fog and carried by the 
steam is not definitely known, but it depends in a large measure 
on the velocity of flow. 

Because of the great difference in weight of water and steam 
nearly all the water can be deposited from a current of steam,. 



§ 340-] THE AMOUNT OF MOISTURE IN STEAM. 439 

in a vessel or reservoir conveniently connected to the steam-pipe, 
by action of gravity or inertia. Such a device is known com- 
mercially as a steam-separator. The water is removed from the 
separator either by an automatically controlled pump or trap or 
by hand. 

In the determination of quality it is desirable to remove the 
free water by a steam-separator before making the connection 
to obtain the sample, as in that case the sample is more likely 
to be an average one. See papers on this subject in the Trans- 
actions of Am. Soc. Mechanical Engineers, Vol. XIII, by Prof. 
D. S. Jacobus, and Vol. XII, by the author. 

MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL 
UNIVERSITY. 

Priming Test with Separator Calorimeter. 

Made by 189. . 

Test of Steam 

at N. Y. 



No. of 
Run. 


Dura- 
tion of 
Run. 


Gauge 
Pressure. 


Absolute 
Pressure. 


Weight of 
Exhaust. 


Weight 
Water. 


Total 

Weight of 

Steam. 


Radia- 
tion- 
loss. 


Mois- 
ture. 


>> 

3 

a 




min. 


lbs. 


P 

lbs. 


•w 
lbs. 


W 

lbs. 


JV-\-w 
lbs. 


R 

lbs. 


1 -X 

per ct. 


X 
per ct. 


I 
2 

3 
4 
5 
6 

7 
8 

9 
10 





















440 EXPERIMENTAL ENGINEERING. [§ 34 1. 

Diameter of orifice in. Area of orifice sq. in. Symbol A. 

Barometer-reading in. 

Formula of instrument, i — x — {W — R) + ( W + w). 
Napier's Rule, Flow of Steam, pounds per second = ^ PA. 

Method of determining R , 

Results 

Method of determining W 

341. The Chemical Calorimeter. — This instrument de- 
pends on the fact that certain soluble salts will not be absorbed 
by dry steam, but will be carried over by water, so that if the 
salt appears in the steam its presence indicates water. 

Various salts have been used, but common salt, chloride of 
sodium, gives as good results as any. 

The proportion that the salt in a given weight of con- 
densed steam bears to that in a given weight of water drawn 
from the boiler, is the percentage of moisture in the steam. 
The method of analysis is a volumetric one, and is as follows : 

Add three or four ounces of common salt to the water in 
the boiler ; after it is dissolved, draw from the boiler a small 
amount of water and condense an equal weight of steam, which 
are to be kept in separate vessels. Add to each of them a few 
drops of neutral chromate of potash, but in each case an equal 
quantity, which amount may be measured by a pipette ; the 
same amount should also be added to a vessel containing an 
equal weight of distilled water, in order to obtain a standard 
or zero-point foi the scale used in the analysis. 

By means of a graduated pipette a triturated solution of 
nitrate of silver is permitted to flow, a single drop at a time, 
into each of the three solutions. The effect is to cause the 
formation of the chloride of silver, and until that formation 
completely takes place the resulting liquid will be whitish or 
milky; but because of the presence of the bichromate, the in- 
stant the chloride has all been precipitated the liquid turns 
red. The amount of nitrate of silver required is measured by 
the graduated pipette, and gives the information regarding the 
salt present. 



§ 34 2 -] THE AMOUNT OF MOISTURE IN STEAM. 



44I 



The detailed directions for the test are as follows : 
Take in each case 100 cubic centimeters of liquid contain- 
ing a few drops of neutral chromate of potassium, and drop 
from a triturated solution holding 10.8 grams of silver to 
the liter ; the following data were obtained in a test : 

AMOUNT OF NITRATE OF SILVER REQUIRED TO TURN 
100 c. c. RED. 



of 



Condensed steam .... 
Water from the boiler 
Distilled water 



First Trial. 



O.I c. c. 
13.6 c. c. 
0.05 c. c. 



Second Trial. 



0.05 c. c. 
14.0 c. c. 
0.05 c. c. 



Third Trial. 



O.I c. c. 

13.35 C. C. 

0.05 c. c. 



Letting the results with these three samples be denoted by 
a, b, and c respectively, and the amount of moisture by 1 — x, 
we have 



x = 



b-c 
This gives the following results : 





First Trial. 


Second Trial. 


Third Trial. 


Amount moisture 


0.1 — 0.05 


0.05 — 0.05 

= 

14.0 — 0.05 


0.1 — 0.05 


13.6 - .05 


i3'35 -0.D5 



Average = 0.0025. 

This method is evidently applicable only in determining 
the amount of moisture in the steam as it leaves the boiler, and 
will give no information regarding the additional moisture that 
may be added to the steam by condensation. 

Instead of common salt, sulphate of soda is sometimes used, 
and the percentage of moisture determined by the percentage 
of sulphuric acid present in the steam as compared with that 
in water from the boiler. 

342. Comparative Value of Calorimeters. — These instru- 
ments, arranged in order of accuracy, are no doubt as follows: 



442 EXPERIMENTAL ENGINEERING. [§ 342. 

throttling ; separating ; Barrus superheating ; Hoadley ; con- 
tinuous condensing ; chemical ; and lastly the barrel. 

The ease with which the throttling and separating instru- 
ments can be used, their small bulk, and great accuracy, render 
them of chief practical importance. 

The throttling calorimeter can be used only for steam with 
a small amount of moisture, as explained in Article 333 ; but 
the separating instrument is not limited by the amount of 
moisture entrained in the steam. It is not, however, as well 
adapted for superheated steam, nor can the results be deter- 
mined as quickly as with the throttling instrument ; when 
carefully handled the accuracy is, however, substantially the 
same. 



CHAPTER XIV. 



DETERMINATION OF THE HEATING VALUE OF FUELS— 
FLUE-GAS ANALYSIS. 



343. Combustion, — Combustion or burning is a rapid 
chemical combination. The only kind of combustion which is 
used to produce heat for engineering purposes is the combina- 
tion of fuel of different kinds with oxygen. In the ordinary 
sense the word combustible implies a capacity of combining 
rapidly with oxygen so as to produce heat. The chief elemen- 
tary constituents of ordinary fuel are carbon and hydrogen. 
Sulphur is another combustible constituent of ordinary fuel, 
but its quantity and its heat-producing power are so small that 
it is of no appreciable value. 

The chemical elements are those which have not been de- 
composed ; these unite with each other in various definite 
proportions, which may be represented by certain numbers 
termed chemical equivalents or atomic weights. These for 
gaseous bodies are very nearly proportional to their densities 
at the same pressure and temperature. 

The atomic weight of a chemical compound equals the sum of 
the atomic weights of all the elements entering into the com- 
bination. Air is not a chemical compound, but a mechanical 
mixture of nitrogen and oxygen. 

The following table gives the properties of the principal 
elementary and compound substances that enter into the com- 
position of ordinary fuels : 



444 



EXPERIMENTAL ENGINEERING. 



[§ 344- 



Substance. 



Oxygen 

Nitrogen 

Hydrogen 

Carbon 

Phosphorus 

Sulphur 

Silicon 

Air...., 

Water 

Ammonia 

Carbonic oxide 

Carbonic acid 

Olefiant gas 

Marsh gas 

Sulphurous acid 

Sulphuretted hydrogen 
Bisulphuret of carbon. 



Symbol. 



O 

N 

H 

C 

P 

S 

Si 

77N 4- 23O 

H 2 

NH 3 

CO 

co 2 

CH 2 

CH 4 

so 2 

SH 2 
S 2 C 



Chemical 
Equivalent 
by Weight. 



16 

M 

I 
12 
31 
32 
14 
IOO 
18 

17 
28 

44 
14 

16 

64 
34 

76 



Chemical 
Equivalent 
by Volume. 



IOO 
2 
2 
2 
2 
2 
2 
2 
2 
2 



Properties of 

Elements 
by Volume. 



79N + 2lO 
H + O 

H + N 



O 

+ o 2 

+ H 2 
+ H 4 
+ 3 
+ H 2 
+ S 2 



344. Calorific Power or Heat of Combustion. — The 

calorific value of a fuel is expressed in British thermal units 
or in calories, according as Fahrenheit or Centigrade therm o- 
metric scales are used. The calorific value may be deter- 
mined by direct experiment, or it may be computed from a 
chemical analysis as follows : 

The carbon is credited with its full heating power, due 
to its complete oxidation as determined by a calorimeter ex- 
periment. The hydrogen is credited with its full heating power, 
after deducting sufficient to form water with the oxygen 
present in the compound ; since when hydrogen and oxygen 
exist in a compound in the proper proportion to form water, 
the combination of these constituents has no effect on the 
total heat of combustion. 

The calorimetric value, determined experimentally, of one 
pound of hydrogen is 62,032 B. T. U. ; that of one pound of 
carbon, 14,500 B. T. U. Hence the combustion of one pound 
of hydrogen is equivalent to that of 4.28 pounds of carbon. 

A formula for the total heat, h, of combustion in B. T. U. 



§ 344-] THE HEATING VALUE OF FUELS. 445 

for each pound of the compound containing hydrogen and 
carbon would be 

^=i 4 ,5oo[c + 4 .28(h --)].. . . , (i) 

For theoretical evaporative power, in pounds of water from 
and at 212 F., 

£ = ^=H.6[C + 4. 2 8(H -§)].. . , ( 2 ) 



The number of pounds of air required to supply the oxygen 
necessary for the combustion of one pound of fuel to C0 2 can 
be computed from the formula 



^ I2 [c + 3 (h-1t)] ; 



. • ,3) 



and the corresponding volume in cubic feet can be found by mul- 
tiplying by the specific volume of one pound at JO degrees Fr. 
In which case the volume in cubic feet is 



«=i 49 [c + 3(h-°)] (4) 



In the above formulae, C, H, and O represent the number 
of pounds respectively of carbon, hydrogen, and oxygen in the 
product of combustion. 

When in the combustion of hydro-carbon fuels in an ordi- 
nary furnace hydrogen is consumed, the water formed passes 
off in the state of vapor, hence the latent heat of evaporation 
is not available. One pound of hydrogen burns to 9 pounds 
of water, the latent heat of which at 21 2° is 966 units; hence 
we must deduct 966 X 9 = 8694 units from the tabular value 



44^ 



EXPERIMENTAL ENGINEERING. 



[§ 345- 



of the heat due to the combustion of hydrogen. This leaves 
53,338 units available. Therefore the actual value in terms of 
carbon is H = 3.67C, instead of 4.28C as stated in (1), and the 
heat of combustion actually available is 



-&=i 4 ,5oo[c + 3.67(h--°)] 



(5) 



The following table gives the heat of combustion of the 
principal combustible substances : 

TOTAL HEAT OF COMBUSTION WITH OXYGEN. 



Substance. 



Hydrogen gas 

Carbon burned to CO 
Carbon burned to CO2. 
Olefiant gas. . , 



Liquid hydro-carbon, 



Sulphur to S0 2 

Silicon to Si0 2 

Phosphorus to P 2 5 

Marsh gas, C 2 H 4 

Crude petroleum 

Oil of turpentine 

Wax 

Ether .... 

Tallow 

Alcohol . . 

Methyl alcohol (wood-spirit). 
Bisulphide of carbon, CS 2 . . . 
Carbonic oxide 



<u c 
^-P • 

O 3 

to £ S 
■a.= o 

C 3U 

o n^! 

n 1- O 



i-33 
2.07 

3-43 



1 

2.29 

1.44 

3-55 
2.8 



1.28 
1-33 



T3 4> 



u O « 

•-Dh p 
<5 .n 

u e 

•+-. 1) o 

o &U 

"■a S 
■a u 1- 

c u efl 

3 '5^ £ 



36 
6 
12 
15-43 



4-5 
10.2 

. 6-5 
16.2 
15-0 



5-7 
6 



CQ* 
Eg 

-Oh 



62,032 

4,400 

14,450 

21,344 
19,000 
21,700 
3,740 
14,000 
10,250 
26,400 
18,600 
19,200 
18,800 
16, ion 
16,000 
12,700 
9,200 
5,750 
IO, IOO 



U U " 

O o 

u 2 



62.6 

4-50 

14.67 
22.1 

20 ) 
22 5 ) 
4.09 
14.24 
10.45 
26.68 
18.53 
19-73 
19.04 
16.41 
16.37 
13.06 

9-65 
6.18 
10.4 



Product of 
Combustion. 



H 2 
CO 

co 2 

C0 2 and H 2 



S0 2 

Si0 2 

p 2 o 5 

CO a and H a O 



<■ n 



«( {( 



CO a and S0 2 
CO a 



345. Determination of the Heating Value by the 
Oxygen required. — It was observed by Welter* that those 



* Chemical Technology, Vol. I., p. 336 : Graves and Thorp. 



§345-] THE HEATING VALUE OF FUELS. 447 

constituents of a compound which require an equal amount of 
oxygen for combustion evolve also equal quantities of heat ; 
from which he concluded that since the oxygen required for 
the combustion of a body is in the same relation as the quan- 
tity of heat evolved, it might fairly be made the measure of 
the heating power. When, therefore, oxygen is consumed by 
the burning of carbon, wood, hydrogen, etc., the heat which 
is evolved must increase with the quantity that is consumed ; 
or the same amount of heat is generated by a certain given 
weight of oxygen, whether that quantity be employed in con- 
verting carbon into carbonic acid, or hydrogen into water. 

The oxygen required is 2§ for one part of carbon ; 8 for one 
part of hydrogen. 

One part by weight of carbon will raise the temperature of 
80.5 parts of water from freezing to boiling. 

One part by weight of hydrogen will raise 234 parts of 
water from freezing to boiling. 

One part by weight of oxygen in burning carbon will heat 

80.5 

— 5- = 29. 1 parts of water. 

One part by weight of oxygen in burning hydrogen will 
heat -2-|A — 29.3 parts of water from the freezing to the boiling 
point. 

In round numbers, therefore, the heating effect of oxygen 
may be assumed as sufficient to raise 29.2 parts of water from 
the freezing to the boiling point. This is equivalent to 2920 
Centigrade heat-units, or to 5230 B. T. U. 

Calorific Value. — The calorific value of the fuel would 
therefore be the product of this number by the number of 
parts of oxygen required. Thus let a equal the number of 
parts of oxygen required for each combustible ; then the heat 
produced by the combustion is 

h = 2920a: in Centigrade units ; 
h = 5230a in B. T. U. 

Thus, for example, in the combustion of carbon to CO,, 



448 EXPERIMENTAL ENGINEERING. |_§ 346, 

2| parts by weight of oxygen are required for ea w *i one of 
carbon ; hence for this case a = 2§ , and 

h— 5230 X 2| = 14,100. 

In the combustion of hydrogen to water 8 parts by weight of 
oxygen are required, and in this case a = 8 ; hence 

h = 5230 X 8 = 41,840. 

This is about two thirds of the actual value of the calorific 
power of hydrogen, but does not differ much from the heat 
available in ordinary combustion. 

In case of a compound body, let a fuel contain a, b, c, and 
d parts by weight of different combustible ingredients ; and 
let «, a x , a 9 , a z be the parts by weight of oxygen required 
by each. Then 

h = 2g2o(aa 4- ba x -f- ca 2 -f- da 3 ) in Centigrade units ; . 
= $2$o{aa -f" & a i + ca i + d a *) m Fahrenheit units. 

346. Temperature produced by Combustion. — In the 

determination of the calorific value of a fuel two principal 
factors are involved, namely, the calorific power, or the total 
amount of heat to be obtained from the perfect combustion of 
its constituents, and the calorific intensity, or the temperature 
attained by the gaseous products of combustion. The calorific 
power will be the same regardless of the method of combustion ; 
that is, a unit of carbon or of hydrogen will give the same heat 
whether burned with the oxygen of the air or of a metallic oxide. 
The calorific intensity or temperature, however, will be greater 
as the volume of gases heated is less. Thus carbon burned to 
C0 2 will produce a much higher temperature when burned in 
oxygen gas than when in the air, since in the latter case it 
must heat an additional quantity of nitrogen equal to rather 
more than three times the weight of the oxygen. 



§346.] THE HEATING VALUE OF FUELS. 449 

The maximum temperature cannot be either computed or 
determined experimentally with complete accuracy, partly be- 
cause the total combustion of a quantity of fuel in a given 
time at one operation is practically impossible, but more par- 
ticularly from the fact that dissociation of gaseous compounds 
produced in burning takes place at temperatures far below 
those indicated as possible by calculation. 

The maximum temperature is calculated as follows : 
The value of one pound of carbon is 8080 Centigrade heat- 
units, or 14,500 B. T. U. The heat absorbed by any body is 
equal to the product of its weight, w, specific heat, s, and rise 
of temperature, t. Hence 

wst = 8080, or t — 8080 -r- ws, in Centigrade degrees, 

and 

t = 14,550 -r- ws, in Fahrenheit degrees. 

In the case of combustion of carbon to CO a in oxygen gas, 
the oxygen required for each part of carbon is 2f parts ; the 
specific heat of C0 2 is 0.216. Hence the maximum temperature 

8080 

= 10,187° C, 



3.67 X 0.216 
or 

3.67 X 0.216 ° ' 

In case it is burned in air an additional weight of 8.88 
pounds of nitrogen, with a specific heat of 0.24, must be 
raised to the temperature of combustion. Hence the maxi- 
mum rise of temperature will be 

8080 
3.67 X 0.216 + 8.888 X 0.24 = 2731 C ° r 486o ° R 

The maximum temperature to be attained by combustion 
of the following substances, as calculated by R. Bunsen, is : 



450 



EXPERIMENTAL ENGINEERING. 



[§ 347- 



Combustible. 


In Oxygen. 


In Air. 


Carbon 


9873° c. 

7067 

9187 

7851 

8061 


17,803° F. 

12,752 

16,568 

14,103 

14,542 


2458° c 

3042 
5413 
5329 
3259 


4456° F. 

5507 
9775 
9624 
5898 


Carbonic oxide, 









If the air supplied to the fuel be in excess of that required 
for perfect combustion, the temperature will be less. 

When the excess of air is 50 per cent, the maximum tem- 
perature from combustion of carbon is 351 5 F. ; when the 
excess is 100 per cent, the maximum temperature is 2710 F. 

The specific heats under constant pressure of the gases usu- 
ally occurring in connection with combustion are 

Carbonic-acid gas 0.2 17 

Steam °475 

Nitrogen 0.245 

Air O.238 

Ashes (probably) O.200 

Oxygen . 0.241 

Carbonic oxide , 0.288 

Hydrogen 0.235 

347. Composition of Fuels. — The fuels in ordinary use 
contain, in addition to the combustible compounds, more or 
less mineral or earthy matter that remains as ash after the 
combustion has taken place ; there is also frequently water in 
the hygroscopic state. The presence of these incombustible 
substances and the fact that perfect combustion can rarely be 
secured tend to make the actual heating effect less than that 
indicated by the theory. The percentage of ash as given in 
various boiler trials shows a wide variation, as follows: 

American coals 5 to 22 percent 

English coals 2.9 to 27.7 " 

Prussian coals 1.5 to 1 1.6 " 

Saxon coals 7.4 to 63.4 " 



348.] 



r FHE HEATING VALUE OF FUELS. 



45* 



The following table gives the composition of the principal 
fuels and the weight of air required to produce perfect com- 
bustion: 

AVERAGE COMPOSITION OF FUELS. 



Fuel. 



Charcoal from wood. 
" from peat. . . 

Coke, good 

Coal, anthracite 

dry bituminous. 

coking 



cannel 

dry, long-flaming... 

lignite 

Peat, dry 

Wood, dry 

" air-dried, 20% H 2 0. 
Mineral oil 



Carbon. 
C 



0-93 

O.80 

O.94 

O.915 

O.87 

O.85 

0.75 

O.84 

O.77 

O.70 

O.58 

O.51 

39- 6 

O.85 



Hydrogen. 
H 



O.035 

O.05 

O.05 

O.05 

0.06 

O.05 

0.05 

O.06 

O.057 

4.8 

O.15 



Oxygen. 
O 



O.026 

O.04 

O.06 

0.05 

0.08 

O.15 

O.20 

O.31 

42,0 

34-8 



Ash. 



0.03 to 0.05 
0.04 to 0.22 



5 to 15 

O.OI 
O.OI 



Pounds of 

Air required 

for one of 

Fuel. 



II. 16 
9.6 

11. 3 

12.13 
12.06 

11-73 

10.58 

11.88 

10.32 

9-30 

7.68 

6.00 

6.00 

15./ 



348. Principle of Fuel-calorimeters. — The caloric value 
of a fuel is determined by its perfect combustion under such 
conditions that the heat evolved can be absorbed and measured. 
It is essential in such cases that (1) the combustion be perfect, 
and that (2) the heat evolved be absorbed and measured. 

The combustion may take place in atmospheric air, in oxy- 
gen gas, or in combination with a chemical that supplies the 
oxygen required. It is essential in all cases that the supply of 
oxygen be adequate for perfect combustion. 

The heat evolved by combustion is determined by the rise 
in temperature of a given weight of water in a calorimeter of 
which the cooling effect, K, has been carefully determined, and 
in which the escaping gases are reduced to the temperature of 
the room. Let w equal the weight of fuel, R the heat evolved 
in heat-units by the combustion of one part, PFthe number of 
parts by weight of water heated from a temperature t' to t. 
Then if the escaping gases be reduced in temperature to that 
of the room, 

wE = (K+ W){t - t'), 



452 EXPERIMENTAL ENGINEERING. 1§35I< 

from which 

B {K+W)(t-f) m 



w 



340. Method of Obtaining Sample of the Fuel.— The 

calorimetric determination is made only on a very small portion 
of the fuel, and care should be exercised to have the se- 
lected sample fairly represent the fuel to be tested. To 
select a sample of coal for calorimetric examination several 
lots of ten pounds each should be chosen from different por- 
tions of the coal to be tested. These should be put in one pile, 
thoroughly mixed, and from the mixture several lots of one 
pound each taken. These latter quantities are to be pulver- 
ized, thoroughly mixed into one pile, and from this the required 
sample selected. It is recommended that the sample be sub- 
jected to a considerable pressure by placing it in a cylinder 
and compressing it by means of a piston moved by hydraulic 
pressure or by a screw : this is of especial importance if the 
fuel is to be burned in oxygen gas, since small particles are 
likely to form an explosive mixture ; and further, soot and tarry 
masses, which under the most favorable circumstances might 
be burned, will be found in the residue. 

350. Heat-equivalent of the Calorimeter. — The effect of 
the calorimeter is most conveniently expressed as equivalent to 
a given weight of water; this is obtained, as for calorimeters 
used in determining the quality of steam (see Article 317, page 
401), either by finding the sum of the products of the weights 
and specific heats of the various constituents of the calorimeter, 
or by comparing the results obtained with those which should 
have been found by the combustion of some fuel whose calo- 
rific power is known — as for instance pure carbon in oxygen 
gas — or again by its cooling effect on steam of known pressure 
3,nd weight, or on warm water as explained on page 372. 

351. Method of Determining Perfect Combustion. — Ths 
quality of the combustion is only to be determined by an 
analysis of the resulting gases and of the products of combus- 
tion. In case of perfect combustion all carbon is reduced tc 



§ 35 2 -J THE HEATING VALUE OF FUELS. 453 

C0 2 , all available hydrogen to water, sulphur to sulphuric acid; 
and further, the sum of the weights of all the products of com- 
bustion should, after deducting the air and oxygen obtained 
from the atmosphere, equal the original weight of the coal. 

The method adopted by Favre and Silbermann * of ascer. 
taining the weight of the substances consumed by calculation 
from the weight of the products of combustion was as follows : 
Carbonic acid was absorbed by caustic potash, carbonic oxide 
was first oxidized to carbonic acid by heated oxide of copper 
and then absorbed by caustic potash ; water vapor was absorbed 
by sulphuric acid. This system showed that it was necessary 
to analyze the products of combustion in order to detect im= 
perfect action. Thus in the case of substances containing car- 
bon, CO was always present to a variable extent with C0 2 , and 
corrections were necessary in order to determine the total 
heat due to the complete combination with oxygen. The 
conclusion arrived at by these experimenters was that in gen- 
eral there was an equality in the heat disengaged or absorbed 
in the respective acts of chemical combination or of decom- 
position of the same elements ; that is, the heat evolved during 
the combination of two simple elements is equal to the heat 
absorbed at the time of the chemical separation, and the quan- 
tity of heat evolved is the measure of the sum of the chemical 
and mechanical work accomplished in the reaction. 

352. Favre and Silbermann's Fuel-calorimeter. — This 
apparatus, as shown in Fig. 208, consisted of a combustion- 
chamber, A, formed of thin copper, gilt internally, and fitted 
with a cover through which solid combustibles could be intro- 
duced into the cage C. The cover was traversed by a tube, E, 
connected bv means of a suitable pipe to a reservoir of the gas 
to be used in combustion, and by a second tube, D, the lower 
end of which was closed with alum and glass, transparent but 
adiathermic substances which permitted a view of the process 
of combustion without any loss of heat. 

For convenience of observation a small inclined mirror was 
placed above the peep-tube D. 

*See Conversion of Heat into Work : Anderson. 



454 



EXPERIMENTAL ENGINEERING. 



[§352. 



The products of combustion were carried off by a pipe, F y 
the lower portion of which constituted a thin copper coil, and 
the upper part was connected to the apparatus in which the 
non-condensible products were collected and examined. The 
whole of this portion of the calorimeter was plunged into a thin 
copper vessel, G, silvered internally and filled with water, which 



■1 



ESSE! 



-8-^-inch- 




TTTTT 



Fig. 208. — Favre and Silbermann's Fuel-calorimeter. 



was kept thoroughly mixed by means of agitators, H. The 
second vessel stood on wooden blocks inside a third .one, /, the 
sides and bottoms of which were covered with swan-skins 
with the down on, and the whole was immersed in a fourth 
vessel,/, filled with water kept at the average temperature of 
the laboratory. Thermometers, K, K, of great delicacy were 



§ 353-] THE HEATING VALUE OF FUELS. 455 

used to measure the increase of temperature in the water sur- 
rounding the combustion-chamber. The quantity of heat 
developed by the combustion of a known weight of fuel was 
determined by the increase of temperature of the water con- 
tained in the vessel G. For finding the calorific value of gases 
only, the cage C was removed and a compound jet, NO, sub- 
stituted for the single gas-pipe, ignition being produced by an 
electric spark or by some spongy platinum fixed at the end of 
the jet. 

353. Thompson's Calorimeter. — Thompson's Calorimeter* 
is often employed for determination of the heating values of 
fuels. It consists of a glass jar graduated to contain 1934 
grams of water; in this are inserted (1) a thermometer to indi- 
cate elevation of temperature, and (2) a cylindrical combustion- 
chamber with a capacity of about 200 grams of water. This 
chamber is capped at the top, and a small tube furnished with a 
valve is screwed into it, to hold the fuel. The combustible to 
be examined, 2 grams, is mixed as intimately as possible with 22 
grams of a very dry mixture of 3 parts of potassic chlorate and 
1 part of potassic nitrate, and introduced into the combus- 
tion-tube ; a nitrate-of-lead fuse is added and lighted. This 
tube is introduced into the combustion-chamber, the cap 
screwed on, and the whole placed without delay in the water 
of the calorimeter. The combustion takes place directly in the 
water, and the gases disengaged rise to the surface. The water 
is proportioned to the fuel as 966 is to 1, so that the rise in 
temperature in degrees F. is proportional to the evaporative 
power. The oxygen required for the combustion is supplied 
by the chemicals added. The water-equivalent of the calorim- 
eter as above described is about ten per cent. When com- 
bustion has ceased, the rise in temperature of the water is 
observed ; to this one tenth is added for the water value of the 
calorimeter. 

The corrected number gives the number of grams of water 
which a gram of the combustible can evaporate. 

*See Chemical Technology, Vol. I. 



45 6 EXPERIMENTAL ENGINEERING. [§ 355- 

354. The Berthier Calorimeter.* — This calorimeter is 
based on the reduction of oxide of lead by the carbon and 
hydrogen of the coal, the amount of lead reduced affording a 
measure of the oxygen expended, whence the heating power 
may be calculated by Welter's law, Article 345. One part of 
pure carbon being capable of reducing 34-J times its weight 
in lead. 

The operation is performed by mixing intimately the 
weighed sample (10 grams) with a large excess of pure litharge 
(400 grains). The mixture, placed in a crucible sufficiently 
capacious to contain three times its bulk, and rendered im- 
pervious to the gases of the furnace by a coating of fire-clay 
or by a glaze, is covered with an equal quantity of pure 
litharge (protoxide of lead). The crucible, being closed with 
a lid and placed on a support in the furnace, is slowly heated to 
redness, and when the gases which cause the mixture to swell 
considerably have escaped, it is covered with fuel and strongly 
heated for about ten minutes, in order to collect the globules 
of lead in a single button. The oxygen from the litharge com- 
bines with and burns the combustible ingredients of the fuel, 
leaving for every equivalent of oxygen consumed an equiva- 
lent of reduced metallic lead. 

The heating power is calculated as follows : 1 part of pure car- 
bon requires 2.666 parts of oxygen by weight, which taken from 
litharge leaves 34.5 parts of metallic lead. The same weight of 
carbon is sufficient to heat 80 parts of water from 32 to 212 . 
Hence every unit of lead reduced by any kind of fuel corre- 

80 
sponds by Welter's law with = 2.23 parts of water raised 

from the freezing to the boiling point. 

355. The Berthelot Calorimeter. — This calorimeter, as 
modified by Hempel, consists of a very strong vessel with a 
capacity of about 250 c.c, into which the fuel is placed after 
being compressed into a solid form ; the combustion is per- 



Chemical Technology, Vol. I., page 337. 



§ 356-] THE HEATING VALUE OF FUELS. 457 

formed in an atmosphere of oxygen gas under a pressure of 10 
to 12 atmospheres.* 

The fuel is ignited by an electric spark, and the heat gen- 
erated is known by measuring the rise in temperature in the sur- 
rounding water, as in the Favre and Silbermann calorimeter. 

The oxygen gas is generated in. a tube about one inch in 
diameter connected to the calorimeter by an intervening tube 
about \ inch in diameter. To this latter tube is attached a 
pressure-gauge to indicate the pressure, and a safety-gauge to 
prevent damage from explosion or excessive pressure. A 
stop-cock is also inserted close to the calorimeter. For gen- 
erating the oxygen the tube is filled with 40 grams of a mix- 
ture of equal parts of manganese dioxide and potassium 
chlorate. It is then heated by the full flame of a Bunsen 
burner applied first at the end nearest the calorimeter and 
gradually moved to the farther end. 

To use the instrument, the fuel, connected to platinum 
wires for electrical ignition, is introduced and suspended in the 
calorimeter, the top of which is firmly screwed on and the 
valve closed. Oxygen gas is then generated until the pressure 
reaches 90 pounds, and exhausted into the air to remove other 
gases from the calorimeter. The escape-valve from the calo- 
rimeter is closed and oxygen gas generated until the pressure- 
gauge shows 150 to 175 pounds pressure per square inch ; then 
the connecting stop-valve is closed and the electric current ap- 
plied. After the heat of combustion has been absorbed the 
determination is made as with the Favre and Silbermann calo- 
rimeter. 

355. The Bomb Calorimeter. — This instrument was 
designed by the French chemist M. Berthelot, and consists 
of a strong steel vessel provided with a tightly fitting cover 
into which the coal is placed for combustion. For the pur- 
pose of combustion an excess of oxygen gas is supplied under 
a pressure of from 20 to 30 atmospheres. The fuel is sup- 
ported by a cage of platinum connected to the cover. The 
fuel is fired by an electric current passing through connecting 

* See Hempel's Gas Analysis, translated by Dennis. 



4^8 



EXPERIMENTA L ENGINEERING. 



[§355. 



wires and generated by a battery of ten bichromate cells. To 
prevent the oxidation of the instrument, the bomb built by 
Berthelot was lined with platinum. The heat given off 
during the process of combustion was absorbed by water in a 
vessel surrounding the bomb. During the process of com- 
bustion this water was kept in motion by a stirrer, and the 
heat given off determined by its rise in temperature. 

Various modifications of coal-calorimeters employing the 
principle of Berthelot's instrument have been made and are 
in extensive use. The form built by Mahler, Fig. 212, is 
perhaps the best known, which differs from that of Berthelot 
only in the form of the stirring apparatus and in the lining of 
the bomb, which is of porcelain enamel, instead of platinum. 
The German chemist Hempel has also designed a bomb 
calorimeter in which the bomb is made of steel, the interior 
of which is protected by an oxidized surface which has been 
found to give practical results. 

The oxygen for use in the calorimeters can be obtained 
from the decomposition of water by electrical means, or it may 




Fig. 209. — Parts of Thompson's Calorimeter in Action. 



be made by heating a crucible filled with equal parts of man- 
ganese dioxide and potassium chlorate- Some chlorine will 
usually pass over, which may be removed by passing through 



§3550 



THE HEATING VALUE OF FUELS. 



459 



a close roll of brass wire-gauze. The oxygen may be 
received into a small gasometer and compressed by the action 
of a pump to the required density. Oxygen is also now- 
manufactured as a commercial article and can be purchased in 
cylinders holding 4 or 5 cubic feet and under a pressure of 20 
atmospheres in nearly all the large cities. Thus it may be 
purchased in New York of Eimer & Amend. 

In the Hempel calorimeter, as shown in Fig. 210, the 
crucible for making the oxygen is attached directly to the 




Fig. 2io.~Hempel's Calorimeter with Enlarged Charging-plug. 

calorimeter by means of connecting pipes. In this case the 
calorimeter is charged before connecting the crucible. The 
crucible is filled with a mixture of equal parts dioxide of 
manganese and chlorate of potash, and the oxygen is driven 
off by the application of heat with the Bunsen burner; the 
heat being first applied at the end of the crucible nearest the 
calorimeter. A pressure-gauge B is connected to the pipe, and 
when the required pressure is reached the burner is removed, 
a connecting stop-cock b closed, and the connections to the 



460 



EXPERIMENTAL ENGINEERING. 



[§ 355. 



crucible removed. To prevent danger from accidents during 
the generation of the oxygen, the crucible and gauge should 
be enclosed in a large wooden vessel. 

The value of the fuel burned is determined from the rise 
in temperature of the water; account being taken of the 
weight of water and also the weights and specific heats of all 
parts of the calorimeter. Usually during combustion some 
nitric acid is formed which is deposited on the walls of "the 
calorimeter. The heat liberated in the formation of nitric 
acid should be taken into account, but as this is seldom greater 
than \ of one per cent, it is usually less than the unavoidable 




Fig. 211.— Charging Calorimeter with Oxygen. 

errors of observation. To avoid the numerous corrections 

and the tedious calculations which result therefrom, the 
chemist Hempel adopted the plan of standardizing his instru- 
ments by burning definite amounts of pure carbon, the value 
of which he took as known from the best investigations by 
Berthelot. To obtain pure carbon with which to standardize 
the instrument, he pulverized and carbonized crystallized 
sugar several times in succession, driving off at a high heat all 
volatile matter. This process of calibration gave a series of 
factors, which multiplied by thermometer-readings reduced 
the results to heat-units. The following example from 



462 



EXPERIMENTAL ENGINEERING. 



VI 355. 



" Traite Pratique de Calorimetre Chimique," by M, Berthe- 
lot, illustrates the process of reduction necessary in using the 
bomb calorimeter. 

The weight of each part of the calorimeter is carefully 
ascertained and multiplied by the specific heat of the material 
composing the part. The sum of these various products gives 
the water equivalent of the calorimeter which is given later. 



DETERMINATION OF THE HEAT IN PURE CARBON. 

Dried at a temperature of from 120 to 130 degrees C. until it had attained a 
constant weight and permitted to cool in a closed vessel and in the presence 
of concentrated sulphuric acid. (Observations of time and temperature,) 



Preliminary Observations 
Before Combustion. 


Observations During 
Combustion. 


Observations After 
Combustion. 


min., 17.360 deg. C. 

1 " 17.360 " 

2 " 17.360 "' 

3 " 17-360 

4 " 17.360 " 


5 
6 

7 

8 


min., 18.500 deg. C. 

" 18.782 

18.820 

11 18.818 


9 
10 
11 
12 
13 
14 


min., 18.810 deg. C. 
" '18.802 
" 18.795 
" 18.785 
" 18.775 
" 18.770 



Initial cooling per minute, zero degrees; final cooling per 
minute, 0.008 deg. C. Total correction for cooling, 0.046 
deg. C. Variation of temperature, not corrected, 18.818 — 
17.360 = 1.438 deg. C. Corrected — 1.484 deg. C. Value in 
water of the calorimeter and contents = 2398. 4gr. Weight of 
nitric acid formed = 0.0173 gr. (Each gram is equal to 227 
calories.) Each gram of iron burned is equal to 1650 calories. 

Total heat observed =3558.5 calories. 

Disengaged by the combustion of the " 

iron-ware 22.4 cal. 

Disengaged by the formation of nitric 

acid 3.9 cal. 

Heat obtained from the combustion of the 



26.3 



carbon = 3532.9 calories. 

3532.2 



Heat for one gram 



0.4342 



8136.6 



§ 35 6 -] rHE HEATING VALUE OF FUELS. 463 

The latest determinations of Berthelot give the absolute 
heating power of amorphous carbon as 8137.4 calories = 
I4629.5 B. T. U. In the use of the calorimeter, the coal 
is to be first powdered and then reduced by pressure to a 
cylindrical cake or lump which is fired by the heat from an 
electric current. Corrections to the result are to be made 
for the heat disengaged by the oxidization of the iron and by 
the formation of nitric acid and by the vapor of water 
remaining in the atmosphere of the bomb. All these correc- 
tions are very small and may be avoided by using the process 
of calibration employed by Hempel. 

As noticed in the example above cited, the rise in tem- 
perature of the surrounding water is very small, and in order 
to obtain accurate results this water must be thoroughly 
agitated to produce a uniform temperature; the thermometer 
used must be capable of reading very small increments of a 
degree and must be read by a strong reading-glass or attached 
vernier. The accurate determination of small increments of 
temperature is nearly impossible with the apparatus to be 
found in an engineering laboratory. To overcome this diffi- 
culty, the author has designed a form of calorimeter in which 
the increase in temperature is determined by the expansion 
of the entire amount of water in the vessel surrounding the 
calorimeter. The value of the scale is determined by calibra- 
tion. Two forms of this instrument are manufactured by 
Schaeffer and Budenberg, Brooklyn, N. Y. In one form the 
combustion is performed in a steel bomb lined with enamel in 
many respects similar to the Mahler calorimeter. In the 
other the combustion is performed in a current of oxygen gas 
under low pressure, and the heat of combustion is absorbed 
by water in the surrounding vessel, the products of combus- 
tion passing through a coil and being finally discharged into 
the atmospheric air. 

356. Fuel-calorimeter in which Heat is Measured by 
Expansion of Water. — The general appearance of the instru- 
ment is shown in Fig. 212; a sectional view of the interior 



464 EXPERIMENTAL ENGINEERING. [§35^ 

part is shown in Fig. 214, from which it is seen that, ir 
principle, the instrument is a large thermometer, in the bulb 
of which combustion takes place, the heat being absorbed by 
the liquid which is within the bulb. The rise in temperature 
is denoted by the height to which a column of liquid rises in 
the attached glass tube. 

In construction, Fig. 214, the instrument consists of a 
chamber, No. 15, which has a removable bottom, shown in 
section in Fig. 213, and in perspective in Fig. 214. The 
chamber is supplied with oxygen for combustion through 
tube 23, 24, 2$, the products of combustion being discharged 
through a spiral lube, 29, 28, 30. 

Surrounding the combustion-chamber is a larger closed 
chamber, 1, Fig. 214, filled with water, and connecting with 
an open glass tube, 9 and 10. Above the water-chamber I 
is a diaphragm, 12, which can be changed in position by 
screw 14 so as to adjust the zero level in the open glass tube 
at any desired point. A glass for observing the process of 
combustion is inserted at 33, in top of the combustion- 
chamber, and also at 34, in top of the water-chamber, and at 
36, in top of outer case. 

This instrument readily slips into an outside case, which 
is nickel-plated and polished on the inside, so as to reduce 
radiation as much as possible. The instrument is supported 
on strips of felting, 5 and 6, Fig. 214. A funnel for filling 
is provided at 37, which can also be used for emptying if 
desired. 

The plug which stops up the bottom of the combustion- 
chamber carries a dish, 22, in which the fuel for combustion 
is placed; also two wires passing through tubes of vulcanized 
fibre, which are adjustable in a vertical direction, and con- 
nected with a thin platinum wire at the ends. These wires 
are connected to an electric current, and used for firing the 
fuel. On the top part of the plug is placed a silver mirror, 
38, to deflect any radiant heat. Through the centre of this 
plug passes a tube, 25, through which the oxygen passes to 



§356.J 



THE HEATING VALUE OF FUELS. 



465 



supply combustion. The plug is made with alternate layers 
of rubber and asbestos fibre, the outside only being of metal, 
which, being in contact with the wall of the water-chamber, 
can transfer little or no heat to the outside. 

The discharge-gases pass through a long coil of copper 





Fig. 213.— Fuel-calorimeter. 



Fig. 214.— Enlarged Section. 



pipe, and are discharged through a very fine orifice in a cap 
at 30. 

The instrument has been so designed that the combustion 
can take place in oxygen gas having considerable pressure, 
and in the form of a bomb; but in practice we have found 
that very reliable results have been obtained with pressures 



466 EXPERIMENTAL ENGINEERING. [§ 35& 

of 2 to 5 pounds per square inch in an instrument of the form 
described, and this has been commonly used in investigations 
at Sibley College. 

For the purpose of making determinations of fuel, oxygen 
gas has been made and stored in a gasometer holding about 
15 cubic feet, from which it was drawn as required. 

Method of Using the Calorimeter. — 1. Select an accurate 
sample by a system of quartering, which shall commence with 
a very great amount, if possible, and finally terminate with a 
very small fraction of a pound. 

2. Reduce to powder by grinding, in a mortar or a mill, 
sufficient coal for several samples. A coffee-mill answers 
excellently for this purpose. 

3. Introduce the sample into a small asbestos cup, drive 
out moisture by warming it over a Bunsen burner or alcohol 
lamp. Weigh accurately on a fine chemical balance-scale. 

4. Introduce the sample into the calorimeter: (a) start 
the oxygen gas flowing; {b) fire the charge, which should be 
done by pressing on a key; (c) at instant coal is lighted, 
throw off the current and note the reading of the scale and 
time. During combustion keep the discharge orifice open, 
occasionally trying it with a small wire. 

5. Watch the combustion, which will usually require 
about ten minutes for each gram of coal, and when completed 
note the scale reading and the time. The difference between 
first and second reading is the actual scale reading. 

6. To correct for radiation note the amount, the water in 
the column has fallen for the same time as required for com- 
bustion ; add this to the actual reading to get the corrected 
scale reading. 

7. Divide the value as shown on the diagram by the 
weight in pounds of the sample burned. The result will be 
the value in B. T. U. of one pound of coal. 

8. Remove the dish in which the combustion took place; 
weigh it carefully with and without contents. If the com- 
bustion has been perfect, the difference of these weights gives 






§ 3 5 6-] THE HEATING VALUE OF FUELS. 467 

the ash. Wipe the combustion-chamber dry for another 
determination. 

9. To prepare for another determination, remove the 
calorimeter from the outside case and immerse in cold water, 
care being taken to prevent any water entering oxygen-tubes 
or combustion-chamber. 

This method is preferable to emptying the calorimeter 
and adding fresh water each time, since the air, which is 
always present in water, will affect the results and is a diffi- 
cult element to remove. The operation of cooling takes but 
a few minutes and is easily performed. 

In order that the instrument may give accurate values, it 
is necessary that all air be removed from the water, and that 
the oxygen be supplied at a constant pressure. The pressure 
with which the instrument was calibrated is given with the 
calibration curve, and if any other pressure is used a new cali- 
bration should be made. 

Do not attempt to use the calorimeter in a room whose 
temperature is above 80 degrees Fahr., as the calorimeter 
should always be warmer than the air of the room. 

In case oxygen is purchased in a condensed form, it can 
be reduced to any desired amount by passing it into a small 
gasometer before reading the calorimeter. The gasometer 
may be made by simply inverting one pail into another which 
is partly filled with water. By weighting the top pail any 
pressure required can be produced. 

If oxygen is made for especial use, it can be received in 
a gasometer, made as described, but with sufficient capacity 
for several tests. 

Oxygen can be made by heating a mixture of about equal 
parts of dioxide of manganese and chlorate of potash placed 
in a closed retort. 

In lighting the platinum wire we use 16 Mesco dry 
batteries connected in four series. A single cell of a storage 
battery, the current of which is ordinarily used for incandes- 
cent lighting, may be used with success. 



468 EXPERIMENTAL ENGINEERING. [§ 356. 

EXAMPLE SHOWING HOW TO DETERMINE THE CALORIFIC 
POWER OF COAL. 

Weight of crucible 1 .269 grams. 

il " and coal. ... ._ 3-0!7 " 

" " and ash 1*567 " 

'combustibles I-450 " 

^ ash 297 << 

" coal 1.747 " 

1.747 reduced to pounds = 1.747 X .002205 = .003852 lbs. 

First scale-reading, 3.90 inches, time 2 o'clock, 55 minutes. 
Second " 14.70 " " 3 " 20 

Third " 14.30 " " 3 " 45 " 

Actual scale reading 3.90 — 14.70 = 10.80 inches. 

For radiation 14.30—14.70= .40 " 

Corrected scale-reading 1 1.2 " 

On the diagram 1 1.2 corresponds to 46.25 B. T. U.'s in 
sample. 

As 46.25 B. T. U. are .00385 lbs., one pound will be: 

46.25 -7- .00385 = 12,000 heat-units. 

All calorimeters are calibrated before shipment, but to 
enable purchasers to make a new calibration in case a new 
glass tube should have to be inserted we give the following 
instructions: 

1. Make a pure coke, reduce some soft coal to powder, 
fill a porcelain or clay crucible 2/3 full, cover it air-tight, glow 
it with a blast-lamp or in a forge-fire for one hour. If cold, 
grind it in a mortar to a very fine powder. Repeat this 
operation. 

2. Remove gland and hexagon plug-screw from top of 
calorimeter and fill it with water. Close the plug-screw and 
connect the glass-tube opening by some rubber hose or glass 
tube with a smaller vessel filled with water. Boil the water 
in the calorimeter body ; this may be done by a Bunsen burner, 
protecting the calorimeter by a thin sheet of asbestos. Place 



§ 35 6 -] THE HEATING VALUE OF FUELS. 469 

the instrument in such a position that the glass-tube opening 
may be its highest point and so enable all air and steam to 
pass through the connection to the smaller vessel. Also keep 
the water in the smaller vessel boiling until the calorimeter 
has fully cooled off. Remove rubber connection, fill the glass 
tube with boiled water and screw it tight. Take care not to 
allow it to pass so far into the calorimeter that air will be 
trapped. 

Put about two inches kerosene oil on top of water-column 
to prevent air from coming in contact with the water. Should 
it be found that the water in column stands too high after the 
calorimeter has taken the temperature of the room, loosen 
the plug and allow water to leak out slowly until the scale- 
reading is about two inches, then close it securely. 

3. If the instrument is ready for calibration, follow in- 
structions given under method of using the calorimeter. The 
difference of weight between the weight of crucible and 
carbon (coke) and the weight of crucible and ash is the 
weight of pure carbon burned. 

Dividing 14540 by the weight of burned carbon, we obtain 
the number of heat-units in the sample. 

By drawing the oblique line on the chart, take the num- 
ber of corrected scale-reading as ordinates, and the number 
of B. T. U.'s in sample as abscissae, make a point on crossing 
and draw a line to zero. 

EXAMPLE OF CALIBRATION. 

Weight of crucible and coke in grams 3.002 

" ash " " I.064 

" burned pure carbon 1.935 

I.935 grams reduced to pound = .00426 lbs. 

1.935 X. 002205 = .00426 lbs. 

14540 X .00426 = 61.86 B. T. U. in sample. 

First scale-reading, 3.33 inches, time 11 o'clock, 15 minutes. 
Second " 16.85 " " II " 40 " 

Third " 16. " " 12 " 10 " 



<< 

(I 



470 EXPERIMENTAL ENGINEERING. [§ 356. 

Actual reading 16.85 — 3-35 = I3-5Q inches. 

For radiation 16.00—16.85= -$5 " 

Corrected scale-reading 14. 35 « « 

" DIRECTIONS FOR PROXIMATE ANALYSIS.* — COAL AND 

COKE." 

The sample should be finely pulverized in a mortar, and 
then thoroughly mixed. 

Moisture. — Place the weighed sample (about 1 gram) in a 
porcelain crucible, and dry in an air-bath for one hour, at a 
temperature between 105 and no degrees C. Weigh as soon 
as cool. Loss is moisture. 

Volatile Matter. — Weigh about \\ grams of the undried 
pulverized coal, place it in a platinum crucible and cover 
tightly. Heat it for 3| minutes over Bunsen burner (bright 
red heat), and then immediately, without cooling, for 3I- 
minutes over blast-lamp (white heat). Cool and weigh. 
Loss, less the moisture, is volatile matter. 

Fixed Carbon. — If a coke be formed in the preceding opera- 
tion, make a note of its properties, color, firmness, etc., then 
place the crucible, with cover removed, in an inclined posi- 
tion, and heat over Bunsen burner until all carbon is burned., 
.i.e., to constant weight. The combustion may be hastened 
by stirring the charge from time to time with a platinum wire. 
Difference between this and last weight is the fixed carbon. 

Ash. — Difference between last weight and weight of cruci- 
ble is the ash. 

Total Sulphur in Coal and Coke. — Prepare a fusing mixture 
by thoroughly mixing two parts calcined magnesia with one 
part anhydrous sodium carbonate. Determine the sulphur 
in the mixture. 

Thoroughly mix I gram of the finely pulverized coal with 
if grams of fusing mixture. Heat over an alcohol lamp, in 
an open platinum or porcelain crucible, so inclined that only 

*See " Crooke's Select Methods," 2d Edition, pp. 595-607. 



g 356.] THE HEATING VALUE OF FUELS. 47 1 

its lower half may be brought to a red heat. The crucible 
should not be over ^ or f full, and the heat should be gentle 
at first, to avoid loss upon the consequent sudden escape of 
volatile matter, if present in large amount. Raise the heat 
gradually (it must not at any time be high enough to fuse the 
mixture), and stir the contents of the crucible every five 
minutes with a platinum wire. The oxidation of the carbon 
is complete when ash becomes yellowish or light gray (about 
one hour). Cool crucible, add 1 gram pulverized NH 4 N0 3 to 
the ash, mix thoroughly by stirring with a glass rod, and heat 
to redness for five to ten minutes, the crucible being covered 
with its lid. 

Cool, digest the mass in water, transfer the crucible con- 
tents to a beaker, rinse out the crucible with dilute warm 
HC1, dilute solution in beaker to about 150 c.c, acidulate 
with HC1, and heat almost to boiling for five minutes. Filter 
and precipitate the sulphuric acid in filtrate by BaCl 2 in usual 
manner. 

Phosphorus. — If present, it will be found in the ash. 
Ignite about 10 grams of the coal in a large platinum crucible, 
and determine the phosphorus in the ash in the usual manner. 
(See Fresenius, p. 741.) 

Sulphur and phosphorus are not usually of importance, un- 
less the coal is destined for certain uses where these ingredients 
would be harmful; the determination requires much more 
time than that of all other processes in the proximate analysis. 

The operation recommended for a mechanical laboratory 
would differ principally from that described, first, in the use 
of larger samples; and second, in the use of porcelain instead 
of platinum crucibles. 

In the determination of the volatile matter the conclusion 
of the operation may be known by change of color in the 
flame. During the operation the flame would be yellow or 
yellowish so long as any volatile matter remained : it would 
then die down, and when the carbon commenced to burn 
would be decidedly blue. The operation to be always stopped 



472 



EXPERIMENTAL ENGINEERING. 



[§ 357- 



soon after the blue flame appears. The crucible recom- 
mended is made of Royal Meissen porcelain, and provided 
with cover. It has a capacity of half an ounce, and costs 
seventeen cents. During the operation the cover is fitted 
snugly in place, and the gases escape around the edge, and 
are kept burning. 

The percentage of ash is determined by weighing the 
residue which remains after combustion in the calorimeter. 
The burning of the fixed carbon requires a long time when 
performed in the air, but in the calorimeter the operation is 
performed very quickly and very accurately, so that the total 
time required to determine the proximate composition and also 
the heat-values of a sample of coal need not exceed twenty 
or thirty minutes, for a person familiar with the operations. 

357. Value of Coal determined by a Boiler-trial. — 
The calorific value of a coal is sometimes determined by the 
amount of water evaporated into dry steam under the con- 
ditions of use in a steam-boiler. This method is fully ex- 
plained in the latter part of the present work in the chapter 
on the methods of testing steam-boilers. The calorific values 
obtained in actual boiler-trials are much less than those ob- 
tained in the calorimeters, because of loss of heat by radiation 
into the air and by discharge of hot gases into the chim- 
ney. The results obtained by such a trial by Prof. W. R. 
Johnson at the Navy Yard, Washington, in 1843, with a small 
cylindrical boiler, were as follows : 





Area of 
Fire- 
grate, 

Sq. Ft. 


Coal per Hour. 


Water evaporated 
per Hour. 


Water 
evaporated 

from 
212 F. per 
lb. of Coal. 


Coal. 


Total. 


Per Sq. 
Ft. of 
Grate. 


Total. 


Per Sq. 
Ft. of 
Grate. 


Anthracite (7 samples). . . 
Bituminous coals, free 

burning (11 samples). . . 
Bituminous coking coals, 

Virginian (10 samples).. 


I4.3O 
I4.I4 
14.15 


94.94 

99.16 

105.02 


6.64 
7.OI 
7.42 


12.37 

13-73 
I2.l6 


O.87 
O.97 
O.86 


9-63 
9.68 
8.48* 




14.20 


99-71 


7.02 


12-75 


O.90 


9.26 





§ 35 8 -] THE HEATING VALUE OF FUELS. 473 

358. Object of Analysis of the Products of Combustion. 

— The products resulting from the combustion of ordinary fuel 
contain principally a mixture of air, C0 2 , and some combus- 
tible gases, as CO and H. To determine whether or not the 
combustion is perfect, it is necessary to know the percentage 
that the combustible gases escaping bear to the total products 
of combustion. It is also important to know whether the air 
supplied is sufficient for the purposes of combustion, and also 
whether it is in excess of the amount actually required. As 
•shown in Article 346, page 448, the presence of an excess of 
air over that required has the effect of lowering the tempera- 
ture of the furnace ; steam would have the same effect even in 
a greater degree, as can readily be shown by calculation. 

From a careful examination of the products of combustion 
we should be able to ascertain its character and make the 
necessary corrections for such losses as may be due to imper- 
fect combustion. 

The methods to be employed must be such as any en- 
gineer can fully comprehend, and the apparatus portable 
and convenient. The degree of accuracy sought need not 
be such as would be required in a chemical laboratory 
where every convenience for accurate work is to be found. 
Indeed, considering the approximations to be made in its ap- 
plication, it is very doubtful if determinations nearer than one 
per cent in volume are required, or even of any value. Such 
determinations are obtained readily with simple instruments, 
and serve to show the. approximate condition of the gaseous 
products of combustion. The student is referred to " Hand- 
book of Technical Gas Analysis," by Clemens Winkler (London, 
John Van Voorst), and to "Methods of Gas Analysis," by Dr. 
W. Hempel, translated by L. M. Dennis (Macmillan & Co.); 
also to a paper on tests of a hot-blast apparatus by J. C. Hoad- 
ley, Vol. VI. Transactions of the American Society of Mechani- 
cal Engineers. 

In a thorough examination of the value of fuel, the ashes 
should also be analyzed, since if they contain any combustible, 



474 EXPERIMENTAL ENGINEERING. [§ 359. 

or partly burned combustible, the heating value must be de- 
termined, and proper allowance made for the same. 

359. General Methods of Flue-gas Analysis. — The 

gases to be sought for are C0 2 , CO, O, and H. Unless the 
temperature is very high, CO is found only in very small 
quantities, and rarely exceeds one per cent. Prof. L. M. 
Dennis, of Cornell University, makes the statement that Dr. 
W. Hempel, of Dresden, whose principal work has been the 
analysis of gases, states that rarely ever is more than a trace of 
carbonic oxide (CO) to be found in the products resulting 
from ordinary combustion. Considering the difficulty of ab- 
sorbing CO, and the consequent errors that are likely to arise, 
it may be in general better to neglect it. The hydrogen, H, 
present is also a very small quantity, unless the temperature 
is abnormally low, and can be neglected without sensible error. 
The analysis may be of two kinds, gravimetrical and 
volumetric. The former is seldom used, but will be found 
described in an article by J. C. Hoadley, Transactions of the 
American Society of Mechanical Engineers, Vol. VI., page 
786. In this case the various gases are passed through solid 
absorbents, and the several constituents successively absorbed 
and weighed. The method of analysis usually adopted is a 
volumetric one, and consists of the following steps, which wiL 
be described in detail later on. 

A. The sample is first collected and then introduced into a 
measuring-tube ; 100 c.c. of the gas is retained, the remainder 
wasted. 

B. The constituents of the gas are then absorbed by suc- 
cessive operations, in the following order : carbonic acid (C0 2 ), 
free oxygen (O), carbonic oxide (CO), and hydrogen (H). 
The absorption is accomplished by causing the gas to flow 
over the reagent in the liquid or solid form, which is introduced 
into the gas or remains permanently in a separate treating- 
tube. It is then made to flow back to the measuring-tube 
and the loss of volume measured. The loss is due to absorp- 
tion, the various absorbents used being as follows : 



§360.] THE HEATING VALUE OF FUELS. 475 

¥ ok carbonic acid, CO,, either potassium hydroxide (caustic 
potash KOH), or barium hydroxide. 

For oxygen, O, either (1) a strong alkaline solution of 
pyrogallic acid, (2) chromous chloride, (3) phosphorus, (4) 
metallic copper. 

For carbon monoxide, CO, either an ammoniacal or a hydro- 
chloric-acid solution of cuprous chloride. 

For hydrogen, H, an explosion or rapid combustion in the 
presence of oxygen, or absorption by metallic potassium, 
sodium, or palladium. The reagent usually employed as an 
absorbent is the one first mentioned in each case. 

360. Preparation of the Reagents.— Absorbents of Oxy- 
gen. — 1. Potassium pyrogallate. This is prepared by mixing 
together, either directly in the absorption pipette or in the 
apparatus, 5 grams of pyrogallic acid dissolved in 15 c.c. of 
water, and 120 grams of caustic potash (KOH) dissolved in 80 
c.c. of water. Caustic potash purified with alcohol should not 
be used for analysis. The absorption of the gas should not be 
carried on at a temperature under 15 C. (55 Fahr.) ; it may 
be completed with certainty in three minutes by shaking the 
gas in contact with the solution. 

2. Chromous chloride will absorb oxygen alone in a mixture 
of oxygen and hydrogen sulphide ; it is prepared with difficulty, 
and not much used. 

3. Phosphorus is one of the most convenient absorbents: 
it is to be kept in the solid form under water and in the dark; 
the gas is to be passed over the reagent, displacing the water, 
and kept in contact with it for about three minutes. The end 
of the absorption is shown by a disappearance of a light glow, 
which characterizes the process of absorption. The phosphorus 
will remain in serviceable condition for a long time. 

4. Copper, at a red heat or in the form of little rolls of wire- 
gauze immersed in a solution of ammonia and ammonium car- 
bonate, is a very active absorbent for oxygen. 

Absorbents of Carbonic Acid (CO,). — i. Caustic potash. 
This solution may be used in varying strengths, depending on 
the method of gas analysis. With the Elliot apparatus, a solu- 



47^ EXPERIMENTAL ENGINEERING. [§ 360. 

tiou of 3 to 5 per cent of KOH in distilled water is sufficiently 
strong, the gas being kept in contact with it for several min- 
utes. When a separate treating-tube is used for each reagent, 
a solution of one part of commercial caustic potash to two 
parts of water is employed. The absorption is accomplished 
very quickly in the latter case, and often bypassing the gas but 
once through the treating-tube. The process is more quickly 
and thoroughly performed by introducing into the treating- 
tubes as many rolls of fine iron-wire gauze as it will hold. 

2. Barium hydroxide in solution is the best absorbent in 
case the quantity of C0 2 is very small ; in this case titration 
with oxalic acid will be required. 

Absorbents of Carbon Monoxide (CO). — i. (a) Hydrochlo- 
ric-acid solution of cuprous chloride is prepared by dissolving 10.3 
grams of copper oxide in 100 to 200 c.c. of concentrated hydro- 
chloric acid, and then allowing the solution to stand in a flask 
of suitable size, filled as full as possible with copper wire, until 
the cupric chloride is reduced to cuprous chloride, and the 
solution is completely colorless. 

(i>) Winkler directs that 86 grams of copper scale be mixed 
with 17 grams of copper powder, prepared by reducing copper 
oxide with hydrogen, and that this mixture be brought slowly 
and with shaking into 1086 grams of hydrochloric acid of 
1. 1 24 specific gravity. A spiral of copper wire is then placed 
in the solution, and the bottle closed with a soft rubber stopper. 
It is dark at first, then becomes colorless, but in contact with 
the air becomes brown. The absorbing power is 4 c.c. of CO. 

The ammoniacial solution is to be used in case hydrogen is 
to be absorbed by palladium. This is prepared from the 
colorless solution (a) as follows : Pour the clear hydrochloric 
acid solution into a large beaker-glass containing i-J to 2 litres 
of waiter, to precipitate the cuprous chloride. After the pre- 
cipitate has settled, pour off the dilute acid as completely as 
of possible, then wash the cuprous chloride with 100 to 150 c.c. 
distilled water, and add ammonia to the solution until the liquid 
takes a pale-blue color. The solutions of cupric chloride de- 
compose readily, and in general should be used when fresh, or 



si 361.] 



THE HEATING VALUE OF FUELS. 



All 



preserved under a layer of petroleum. The treating-tube con- 
taining the reagent is frequently supplied with spirals of small 
copper wire which tend to preserve and increase the absorb- 
ing capacity of this reagent. 

361. Method of obtaining a Sample of the Gas. — In 
order to take a sample of the gas for analysis from any place, 
such as a furnace, flue, or chimney, an aspirating-tube is intro- 
duced into the flue : this consists of a tube open at both ends, 
the outside end being provided with a stop-cock and connected 
with the collecting apparatus by an india-rubber tube. There 

mm 






-■ 



'M 



Mm 




Fig. 215.— Hoadley's Flue-gas Sampler. 

is probably a great diversity in the composition of gases from 
various parts of the flue. 

For obtaining an average sample, J. C. Hoadley employed 
a mixing-box B* provided with a large number of J-inch pipes, 
ending in various parts of the cross-section of the flue A. An 
elevation of the mixing-box is shown at B' . From the mix- 
ing-box four tubes CC lead downward from various parts to a 
mixing-chamber D, from which a pipe E leads to the collecting 
apparatus. Two of these mixing-boxes were used, one placed 
in the flue a short distance above the other, and an agreement 
of the samples obtained from each was regarded as proof of the 
substantial accuracy of the sample. 

* Trans. Am. Soc. M. E., Vol. VI. 



4/8 EXPERIMENTAL ENGINEERING. [§ 36 1. 

It is hardly probable that a tube furnished with various 
branches or a long slit will give a fair sample, since the velocity 
of gases in the aspirating-tube is such that most of the gas 
will be collected at the openings nearest the collecting appa- 
ratus ; the author has often employed a branch-tube with holes 
opening in different portions of the chimney. The material 
for the aspirating-tube is preferably porcelain or glass, but 
iron has no especial absorptive action on the gases usually to 
be found in the flue, and may be used with satisfaction. A long 
length of rubber tubing may, however, sensibly affect the 
results. 

The gas should be collected as closely as possible to 
the furnace, since it is liable to be diluted to a considerable 
extent by infiltration of air through the brick-work beyond 
the furnace. 

In order to induce the gas to flow outward and into the 
collecting apparatus, pressure in the collecting vessel, termed 
an aspirator, must be reduced below that in the flue. This is 
accomplished by using for an aspirator two large bottles con- 
nected together by rubber tubing near the bottom, or better 
still, two galvanized iron tanks, about 6 inches diameter and 
2 feet high, connected near the bottom by a rubber tube, in 
which is a stop-cock; one of the bottles or tanks has a closed 
top and a connection for rubber tubing provided with stop- 
cock at the top ; the other bottle or tank is open to the atmos- 
phere. To use the aspirator, the vessel with the closed top is 
filled with water by elevating the other vessel ; it is then con- 
nected to the aspirating-tube, the open vessel being held so 
high that it will remain nearly empty. After the connection is 
made, and the stop-cocks opened, the empty vessel is brought 
below the level of the full one, and the water passing from 
the one connected to the aspirating-tube lessens the pres- 
sure to such an extent that it will be filled with gas. This 
process should be repeated several times in order to in- 
sure the thorough removal of all air from the aspirating- 
tubes. The liquid used for this purpose is generally water, 
which is an absorbent to a considerable extent of the gases 



§ 3 6 3-J THE HEATING VALUE OF FUELS. 479 

contained in the flues. To lessen its absorbent power, the 
water used should be shaken intimately with the gas in order 
to saturate it before the sample for analysis is taken. When 
mercury is used as the liquid this precaution is not necessary. 

A small instrument, on the principle of an injector, in which 
a small stream of water or mercury is constantly delivered, is 
an efficient aspirator, and is extremely convenient for continu- 
ous analysis. 

362. General Forms of Apparatus employed for Volu- 
metric Gas Analysis. — The apparatus employed for volumetric 
gas analysis consists of a measuring-tube, in which the volume 
of gas can be drawn and accurately measured at a given press- 
ure, and a treating tube into which the gases are introduced 
and then brought in contact with the various reagents already 
described. The apparatus employed may be divided into two 
classes: (1) those in which there is but one treating-tube, the 
different reagents being successively introduced into the same 
tube ; (2) those in which there are as many treating-tubes as 
there are reagents to be employed, the reagents being used in 
a concentrated form, and the gases brought into contact with 
the required reagent by passing them into the special treating 
tube. 

In either case the steps are, as explained in Article 358: {a) 
Obtain 100 c.c. by measurement; (b) to absorb the C0 2 , bring 
the gas in contact with KOH, and measure the reduction of 
volume so caused ; this is equivalent to the percentage of C0 2 ; 

(c) bring the gas in contact with pyrogallic acid and KOH, and 
absorb the free oxygen. Measure the reduction of volume so 
caused ; this is equivalent to the percentage of free oxygen ; 

(d) determine the other constituents in a similar manner. 

In performing these various operations it is essential that 
the tubes be kept clean and that the reagents be kept entirely 
separate from each other. This is accomplished by washing or 
causing some water to pass up and down the tubes or pipettes 
several times after each operation. 

363. Elliot's Apparatus. — This is one of the most simple 
outfits for gas analysis, and consists of a treating-tube AB and 



480 



EXPERIMENTAL ENGINEERING. 



[§ 363. 




Fig. 216.— Elliot's 
Apparatus. 



a measuring-tube A'B', Fig. 216, connected by a capillary tube 
at the top, in which is a stop-cock, G. The tubes shown in Fig. 
163 are set in a frame-work having an upper and a lower shelf, 
on which the bottles L and K can be placed. In using the 
apparatus, it is first washed, which is done by 
filling the bottles with water, opening the 
stop-cocks F and G, and alternately raising 
and lowering the bottles K and L. The 
bottles are then filled with clean distilled 
water, raised to the positions shown, and the 
stop-cocks G and F closed. The gas is then 
introduced by connecting the discharge from 
the aspirator to the stem of the three-way- 
cock F, and turning it so that its hollow stem 
is in connection with the interior of the tube 
AB ; lowering the bottle L, the water will flow out from the 
tube AB and the gas will flow in. When the tube AB is full 
of gas the cock F is closed, the aspirator is disconnected, and 
the gas is measured. The gas must be measured at atmos- 
pheric pressure. That may be done by holding the bottle in 
such a position that the surface of the water in the bottle shall 
be of the same height as that in the tube. A distinct meniscus 
will be formed by the surface of the water in the tube ; the 
reading must in each case be made to the bottom of the 
meniscus. To measure the gas, which will be considerably in 
excess of that needed, the cock G is opened, the bottle ^de- 
pressed, the bottle L elevated ; the gas will then pass over into 
the measuring-tube A'B' ; the bottle K is then held so that the 
surface of the water shall be at the same level as in the measuring- 
tube, and the bottle L manipulated until exactly 100 c. c. are 
in the measuring-tube ; then the cock G is closed, the cock F 
opened, the bottle L raised, and the remaining gas wasted, 
causing a little water to flow out each time to clean the con- 
necting tubes. The measuring-tube A'B' is surrounded with a 
jacket of water to maintain the gas at the uniform temperature 
of the room. After measuring the sample it is then run over 
into the treating-tube AB, and the reagent introduced through 



365-j 



THE HEATING VALUE OF FUELS. 



481 



the funnel above F by letting it drip very slowly into the tube 
AB. After there is no farther absorption in the tube AB, the 
cock F is closed and the gas again passed over to the measur- 
ing-tube^^, and its loss of volume measured. This operation 
is repeated until all the reagents have been used ; in each case, 
when the gas is run back from the measuring-tube, pass over 
a little water to wash out the connections ; exercise great care 
that in manipulating the cocks K or G no gas be allowed to 
escape or air to enter. 

364. Wilson's Apparatus .*— This apparatus is illustrated 
in Fig. 217. It is used in essentially the same manner as the 
Elliot apparatus, mercury being used as the displacing liquid 
in place of water. It consists of 

a treating-tube d, a measuring- 
tube a, connected at the top by a 
capillary tube f. The measuring- 
tube ends in a vessel filled with 
mercury, and in this case the press- 
ure on the tubes can be regulated 
by lowering and raising the single 
bottle filled with mercury, and the 
gas can be manipulated as in the 
Elliot apparatus, using one bottle 
instead of two. Reagents are in- 
troduced into the funnel e y and 
come in contact with the gas in 
the treating-tube d. 

The collecting-tube used with 
this apparatus is shown at B, and 
consists of a vessel filled with mer- 
cury. One side is connected to 
the aspirator -tube ; some of the 
mercury is allowed to run out 
through a cock, and the space is filled by the gas. Sufficient 
mercury is retained to form a seal. 

365. Fisher's Modification of Orsat's Apparatus. — This 

* Thurston's Engine and Boiler Trials, p. 107. 




Fig. 217. — Apparatus for Gas Analysis. 



482 



EXPERIMENTAL ENGINEERING. 



[§ 365. 



apparatus, shown in Fig. 218, belongs to the class in which 
each reagent is introduced in a concentrated form into a special 
treating-tube. The apparatus consists of a measuring-tube 
surrounded by a water-jacket, into which the gas can be intro- 
duced substantially as explained for the Elliot apparatus. Each 




Fig. 218.— Orsat's Gas-analysis Apparatus. 



reagent is introduced in a concentrated form into a pair of 
burettes connected at the bottom by a U-shaped tube. 

In making an analysis the gas is first drawn into the 
measuring-tube and 100 c.c. retained ; the cock in the tube 
leading to one of the treating-tubes is then opened, the bottle 
raised, and the gas driven over into the treating-tube. This 



§366.] THE HEATING VALUE OF FUELS. 483 

operation is facilitated by connecting a soft rubber bag to 
the opposite side of the treating-tube, by means of which 
alternate pressure and suction can be applied, and the reagent 
protected from the atmosphere. After the absorption is com- 
plete, which will take from one to three minutes in each tube, 
the gas is returned to the measuring-tube by lowering the 
bottle and exerting pressure on the attached rubber bag. The 
rubbei bag is not shown in Fig. 218, and is not required, pro- 
vided the treating-tube is completely filled with the reagent 
on the side toward the measuring-tube. 

The treating-tubes are filled in order from the measuring- 
tube with the following reagents: (1) with 33 per cent solution 
of KOH ; (2) with a solution of pyrogallic acid and KOH, 
or with sticks of phosphorus (see Article 360) ; (3) with a 
hydrochloric-acid or an ammoniacal solution of cuprous chloride 
in contact with copper wire (see Article 359). 

In the first treating-tube is absorbed C0 2 , in*the second O, 
ard in the third CO. 

A modification of the Orsat apparatus has a fourth tube in 
wnich hydrogen can be exploded ; the reduction in volume, due 
to the explosion, gives the amount of hydrogen present. 

An apparatus for flue-gas analysis has been designed by 
the author in which the treating-tubes are arranged as in the 
Orsat, but they are of such a form as to permit the use of solid 
reagents for absorbing oxygen, and are much less liable to 
rupture. It is used exactly as described for the Orsat, but is 
much more convenient and is somewhat more accurate. 

366. Hempel's Apparatus for Gas Analysis.* — This ap- 
paratus, shown in Figs. 219 to 224, is especially designed for 
the accurate analysis of the constituents of various gases ; for 
laboratory use it presents many advantages over the other 
apparatus described. The apparatus consists of the following 
parts : I. The measuring burette, shown in Fig. 220, which is 
constructed and used as follows : It is furnished with an iron 



*See Hempel's Gas Analysis, by L. M. Dennis. Catalogue of Eimer & 
Amend, New York. 



4^4 



EXPERIMENTAL ENGINEERING. 



[§ 366. 



base, which is connected by a rubber tube to an open tube a 
(see Fig. 219) with a similar base. The stop-cock d is opened, 
the tube a elevated, and water or mercury, whichever may be 



Fig. 219. 




Fig. 



used, flows from a over to b. Gas is introduced as follows: 
The measuring-tube b is filled with liquid, the cocks d and c 
closed, and connection made at e to the vessel containing the 
gas to be measured ; the cocks d and c are then opened, the 



§ 366.] 



THE HEATING VALUE OF FUELS. 



4 3 5 



tube a lowered ; the liquid will then flow from the measuring- 
tube b to a, and the gas will fill the measuring-tube. To meas- 
ure the volume of gas, hold the tube a as shown in Fig. 219, so 
that the water-level shall be the same in both tubes^ thus 
bringing the gas under atmospheric pressure. Read the vol- 




FlG. 221. 





Fig. 222. 




Figs. 223-224. — Hempel's Absorption Burettes. 



ume directly by the graduation corresponding to the lower 
edge of the meniscus. 

The absorption-pipettes are different in form from those used 
in the Orsat apparatus, and are connected only as required to 
the measuring-burette, but are used in essentially the same 
way. Several forms of these are employed as shown in Figs. 
221 to 224. The forms shown in Fig. 222 and Fig. 224 are 



486 EXPERIMENTAL ENGINEERING. [§ 367 

ordinarily used for reagents in solution. In such a case the 
measuring-tube is connected at e, Fig. 222, the reagent occupy- 
ing the bulbs a and b. The top of the measuring-burette 
e, Fig. 219, is connected to the absorption-pipette, and the 
gas moved alternately forward and backward as required by 
raising or lowering the tube a. In case reagents in the solid 
form are to be used, the absorption-pipette is made of the form 
shown in Fig. 223, in case regents which decompose very easily 
are used a pipette of the form shown in Fig. 221 is employed. 
The general methods employed are the same as those pre- 
viously described. 

367. Deductions and Computations from Flue-gas 
Analysis. — The determinations give the percentage of volume 
of C0 2 , O, and CO existing in the products of combustion. 
Of these constituents the carbon is derived entirely from the 
fuel and the oxygen in great part from the atmosphere. Every 
part of oxygen drawn in from the atmosphere brings with it 
nitrogen, which passes through the furnace unchanged. The 
nitrogen is calculated as follows : The proportion of nitrogen 
to oxygen existing in the atmosphere is 79 to 21 by volume; 
call this ratio S\ denote the percentage of volume of the gases 
existing in the sample as follows : C0 2 by K', oxygen by 0\ 
CO by U'j nitrogen by N'. Then we shall have 

K'+0'+ U'+N'= 100 per cent, . . . (1) 
from which 

N f = 100 - {K' + a + uy .... (2) 

If the oxygen were all derived from the atmosphere, both 
the amount of nitrogen N' and of carbonic oxide U' could be 
computed, since in such a case the volume occupied by the 
free oxygen before combining would equal 

K'+O' + W. 

Hence the nitrogen 

N" = S{K' + 0' + i[/'y . .... . . (3) 



§ 367.] THE HEATING VALUE OF FUELS. 487 

Substituting this latter value in equation (1), 

K* + a + u f + s(K r + a+W) = 100, 

from which 

U'={i*>-{K'+0')(i+S)\+[i + S). . (4) 

Since there is to be found from 2 to 5 per cent of oxygen 
in the fuel, equation (4) will generally give negative values for 
the CO, and should not be used. 

The composition of the flue-gases is an index of the com- 
pleteness of the combustion. The flue-gases should contain 
only nitrogen, oxygen, steam, and carbon dioxide, if the com- 
bustion is perfect. Since the amount of CO and of hydrogen 
compounds are always small, the excess of air can be com- 
puted very nearly from the amount of C0 3 . Thus, were the 
products of combustion free oxygen, nitrogen, and carbon 
dioxide, only, the volume of oxygen and carbon dioxide 
would replace that of oxygen in the air, or would equal about 
20.8 per cent. On account of slight losses, it is more nearly 
20 in actual cases. The percentage of excess of air would 
then be 20 less the per cent of carbon dioxide divided by the 
percentage of carbon dioxide, 

20 - k ' / X 

y=~v- (5) 

Siegert gives an approximate formula for the percentage of 

heat lost, 

T — t 
V x = 0.65 rn = in centigrade units, (6) 

in which T= temperature of the flue; 

t = temperature of air entering furnace, 
C0„ = percentage of C0 2 . 

The principal object of the flue-gas analysis may be con- 
sidered as accomplished when the percentage of uncombined 



488 EXPERIMENTAL ENGINEERING. [§ 3^7- 

oxygen and of C0 2 is determined, since in every case the 
amount of the ether gases present will be very small. From 
these we can find the ratio of the total oxygen supplied to 
that used. This ratio, which is called the dilution coefficient X, 
shows the volume of air supplied to that required to furnish 
the oxygen for the combustion. 

It may be computed by comparing the total volume of 
gases with that required to unite with the combined oxygen, 
from which 

= N'-so' " I 1 + ~K r r nearly * • * (7) 



The analysis and the computations considered relate to 
volumes of the various gases. They may be reduced to pro- 
portional weights by multiplying the volume of each gas by its 
molecular weight and dividing by the total weights. Knowing 
the proportional weights for each gas and the total carbon 
consumed, the total air passing through the furnace can be 
computed. Thus for the perfect combusrion of a pound of 
carbon will be required 2.67 pounds of oxygen, for which will 
be required 11.7 pounds of air. If the ratio of air used to that 
required be X, then the weight of air per pound of fuel equal 
11. yX. One pound of air at 32 Fahr. occupies 12.5 cubic feet. 
Knowing which, the volume of air per pound of coal can be 
computed as equal 

12.5 X 11.7X— 146.2X 

The maximum temperature T m , that can possibly be attained 
in the furnace, is to be calculated as in Article 346, page 449. 



r _ 14500 

m ~ (3.67X0.216) + (8.88X0.24) + (X- i)(i2.6)(o.238> 

14500 5000 . . 1 

= 2.91+ 2.8 4 (X - 1) = -JT a PP ro *' matel y- • • (8) 



§ 368.] THE HEATING VALUE OF FUELS, 489 

Having the maximum temperature of the furnace and the 
temperature of the escaping gases, the efficiency, ■£, of the 
boiler and grate may be calculated by the formula 

E= - ~ , (9) 

in which TJ is the excess of temperature of the furnace and 
T f the excess of temperature of the escaping gases above that 
of the entering air. This hypothesis would be strictly true 
were there no loss of heat and were the weight of entering and 
discharge gases the same. The error in the calculation is not 
usually a serious one. 

Rankine, in his work on the steam-engine, pages 287 and 
288, gives formulae for computing velocity of flow in flues, 
the head required to produce a given reading of the draught- 
gauge, and the required height of chimney. 

These formulae are developed from the experimental work 
of Peclet, and while they do not agree well with modern 
practice, still give interesting results for comparison. The 
practical application is shown in the following example of an 
analysis made at Cornell University, the coal burned being that 
obtained after deducting ashes and clinkers. 

368. Form for Data and Computations in Flue-gas 
Analysis. — Test made Nov. 3, 1890. 

Determinations made by F. Land, H. B. Clarke, and O. G. Heilman. 
Location of plant, Ithaca, N. Y. 
Owners, Cornell University. 

Area of grate, so, ft 181 

Area of chimney, so. ft. (symbol A) 12.5 

Height of chimney, in feet (symbol H') 100 

Length of heated flue (symbol /), feet ....,.« 130 

Inside perimeter of chimney, feet 14 

Ntimbet of boilers . . . , 3 

Size of boilers : one of 61 H. P., two of 250 H. P. 

Kind of boilers : Water-tube, made by Babcock & Wilcox. 

Character of draught, forced by steam-blowers. 



49Q 



EXPERIMENTAL ENGINEERING. 



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CHAPTER XV. 
METHODS OF TESTING STEAM-BOILERS. 

369. Object of Testing Steam-boilers. — The object of 
the test must be clearly perceived in the outset ; it may be to 
determine the efficiency of a given boiler under given condi- 
tions; the comparative value of various fuels, or of different 
boilers working under the same conditions ; or the quantity of 
coal consumed and water used in providing steam for a given 
engine. The results of the test are usually expressed in pounds 
of water evaporated for one pound of the fuel used. 

The conditions of temperature and pressure between which 
boilers work vary within wide limits, the amount of heat ab- 
sorbed per pound of steam produced is not constant, and a 
standard of reference is necessary. Thus to convert a pound 
of steam from feed-water at a temperature of 70 degrees Fahr. 
»nto steam at 70 pounds absolute pressure per square inch will 
require, per pound of steam, (1 174.3 — 70 -(- 32) = 1 136.3 
B. T. U. ; but to convert a pound of water at a temperature of 
212 into steam at atmospheric pressure will require only 967 
B. T. U. To compare the work done with a standard con- 
dition it is customary to express the, results of the test as 
equivalent to the evaporation per pound of fuel from water 
at 212 Fahr. to steam at atmospheric pressure, or, in other 
words, " from and at 212 ." 

The fuel also varies greatly in its evaporative power, as 
shown in the preceding chapter, and, moreover, a certain propor- 
tion is likely to drop through the grates unconsumed, so that 

492 



§ 37 1 -] METHODS OF TESTING STEAM-BOILERS. 493 

it is customary to reduce the results still further, and to find 
the evaporation per pound of the combustible part. 

370. Definitions. — The following terms are frequently 
used : 

Actual evaporation. This is the evaporation per pound of 
fuel or of combustible under the actual conditions of the test, 
uncorrected for temperature of feed-water and for moisture. 

Equivalent evaporation from and at 21 2° is the amount of 
water that would have been evaporated had the temperature 
of feed-water been 21 2°, the steam dry and at atmospheric 
pressure. If x represent the quality of steam, e the factor of 
evaporation, the equivalent evaporation is equal to the actual 
multiplied by xe. 

Factor of evaporation is the ratio that the total heat, A, in 
one pound of steam at the given pressure and reckoned from 
the temperature, /, of feed-water, bears to the latent heat 
of evaporation at 212°, r. That is, 

X-t + 32 



A table of the factors of evaporation is given in the Appendix. 

The ash is the actual incombustible part of the coal ; it is 
the residue which falls through the grates, less any combustible 
particles. 

The combustible is the fuel less the residue which falls 
through the grates ; it is the weight of that portion actually 
burned. In the absence of any determinations whatever, the 
combustible is frequently assumed as f of that of the coal. 

The quality of the steam is the percentage by weight of 
dry saturated steam in a mixture of steam and water. It is to 
be found by a throttling or separating calorimeter attached 
very near the boiler (see Articles 334 to 338). 

371. The Efficiency of a Boiler.— The efficiency is the 
ratio of the heat utilized to that supplied. The heat supplied 
is measured by the coal consumed, multiplied by the heat 
value per pound. 



494 EXPERIMENTAL ENGINEERING. [§ 37 2 

There are in use two methods of denning and calculating 
the efficiency of a boiler. They are: 

^,-c . r ^i i_ -i Heat absorbed per lb. combustible 

1. Efficiency of the boiler = .— : 1- • 

Heating value of I lb. combustible 

2. Efficiency of the boiler and grate 

_ Heat absorbed per lb. coal 
Heating value of I lb. coal 

The first of these is sometimes called the efficiency based 
on combustible, and the second the efficiency based on coal. 
The first is recommended as a standard of comparison for all 
tests, and this is the one which is understood to be referred 
to when the word " efficiency" alone, is used without qualifica- 
tion. The second, however, should be included in a report 
of a test, together with the first, whenever the object of the 
test is to determine the efficiency of the boiler and furnace 
together with the grate (or mechanical stoker), or to com- 
pare different furnaces, grates, fuels, or methods of firing. 

In calculating the efficiency where the coal contains an ap- 
preciable amount of surface moisture, allowance is to be made 
for the heat lost in evaporating this moisture by adding to the 
heat absorbed by the boiler the heat of evaporation thus lost. 

372. The Heat-balance. — An approximate ''heat-bal- 
ance, or statement of the distribution of the heating value of 
the coal among the several items of heat utilized and heat 
lost should be included in the report of a test when analyses 
of the fuel and of the chimney-gases have been made. This 
should show both in B.T.U. and in per-cent the total heat 
received, that absorbed by the boiler, discharged in the flue 
with the products of combustion, that lost in evaporating 
moisture in the combustible, that due to incomplete combus- 
tion of carbon or hydrogen, and that not accounted for. 

373. Horse-power of a Boiler. — The horse-power of a 
boiler is a conventional definition of capacity, since the boiler 
of itself does no work. As the weight of steam required for 
different engines varies within wide limits, an arbitrary rating 
was adopted by the judges of the Centennial Exhibition in 



I 375-] METHODS OF TESTING STEAM-BOILERS. 



495 



1876 as a standard nominal horse-power for boilers. This 
standard, which is now generally used, fixed one horse-power 
as equivalent to 30 pounds of water evaporated into dry steam 
per hour from feed-water at ioo° Fakr., and under a pressure of 
seventy pounds per square inch above the atmosphere. This is 
equal to an evaporation of 34.488 pounds from and at 21 2° F. 
The " unit of evaporation " being 966.7 B. T. U., the commer- 
cial horse-power is 34.488 X 966.7 ==' 33,391 B. T. U. 

374. Graphical Log. — The results of a boiler-test can be 
represented graphically by considering intervals of time as 
proportional to the abscissae, and ordinates as proportional to 
the various pressures and temperatures measured, as shown in 
Fig. 225, from Thurston's Engine and Boiler Trials. 



Indicated Horse Power 




.(9216.1) 



1.3010.50 11.10 11.30 11.60 12.10 12.30 12.50 1.10 1.30 1.50 2.10 2.30 2.50 3.10 3.30 3.50 4.10 .4.30 4.50 

Fig. 225. 



375. Method of Making a Boiler-test— A standard 
method of making a boiler-test was adopted by the American 
Society of Mechanical Engineers in 1884; this was revised in 
1899. The first report is published in the Transactions, Vol. 
VI, the latter in Vol. XXI, with discussion on the same as 
appendices. 



49 6 EXPERIMENTAL ENGINEERING. [§ 375 

EULES FOE CONDUCTING BOILEE TEIALS. 

CODE OF 1899. 

I. Determine at the outset the specific object of the proposed 
trial, whether it be to ascertain the capacity of the boiler, its 
efficiency as a steam generator, its efficiency and its defects under 
usual working conditions, the economy of some particular kind 
of fuel, or the effect of changes of design, proportion, or opera- 
tion ; and prepare for the trial accordingly. (Appendix II.) 

II. Examine the boiler, both outside and inside ; ascertain the 
dimensions of grates, heating surfaces, and all important parts ; 
and make a full record, describing the same, and illustrating 
special features by sketches. The area of heating surface is to 
be computed from the surfaces of shells, tubes, furnaces, and fire- 
boxes in contact with the fire or hot gases. The outside diam- 
eter of water-tubes and the inside diameter of fire-tubes are 
to be used in the computation. All surfaces below the mean 
water level which have water on one side and products of com- 
bustion on the other are to be considered as water-heating 
surface, and all surfaces above the mean water level which 
have steam on one side and products of combustion on the 
other are to be considered as superheating surface. 

IIL Notice the general condition of the boiler and its equipment, 
and record such facts in relation thereto as bear upon the objects 
in view. 

If the object of the trial is to ascertain the maximum economy 
or capacity of the boiler as a steam generator, the boiler and all 
its appurtenances should be put in first-class condition. Clean 
the heating surface inside and outside, remove clinkers from 
the grates and from the sides of the furnace. Eemove all dust, 
soot, and ashes from the chambers, smoke connections, and 
flues. Close air leaks in the masonry and poorly fitted clean- 
ing doors. See that the damper will open wide and close tight. 
Test for air leaks by firing a few shovels of smoky fuel and im- 
mediately closing the damper, observing the escape of smoke 
through the crevices, or by passing the flame of a candle over 
cracks in the brickwork. 

IV. Determine the character of the coal to be used. For tests 
of the efficiency or capacity of the boiler for comparison with 
other boilers the coal should, if possible, be of some kind which 
is commercially regarded as a standard. For New England 



§ 375-] TESTING STEAM-BOILERS. 497 

and that portion of the country east of the Allegheny Moun- 
tains, good anthracite egg coal, containing not over 10 per cent, 
of ash, and semi-bituminous Clearfield (Pa.), Cumberland (Md.), 
and Pocahontas (Va.) coals are thus regarded. West of the 
Allegheny Mountains, Pocahontas (Va.) and New Kiver (W. Va.) 
semi-bituminous, and Toughiogheny or Pittsburg bituminous 
coals are recognized as standards.* There is no special grade 
of coal mined in the Western States which is widely recognized 
as of superior quality or considered as a standard coal for 
boiler testing. Big Muddy lump, an Illinois coal mined in 
Jackson County, 111., is suggested as being of sufficiently high 
grade to answer these requirements in districts where it is more 
conveniently obtainable than the other coals mentioned above. 

For tests made to determine the performance of a boiler with 
a particular kind of coal, such as may be specified in a contract 
for the sale of a boiler, the coal used should not be higher in 
ash and in moisture than that specified, since increase in ash 
and moisture above a stated amount is apt to cause a falling off 
of both capacity and economy in greater proportion than the 
proportion of such increase. 

V. Establish the correctness of all apparatus used in the test for 
weighing and measuring. These are : 

1. Scales for weighing coal, ashes, and water. 

2. Tanks, or water meters for measuring water. Water me- 
ters, as a rule, should only be used as a check on other measure- 
ments. For accurate work, the water should be weighed or 
measured in a tank. (See Chapter VII.) 

3. Thermometers and pyrometers for taking temperatures of 
air, steam, feed-water, waste gases, etc. (Chapter XII.) 

4. Pressure-gauges, draught-gauges, etc. (Chapter XI, pages 
345 to 369.) 

The kind and location of the various pieces of testing appara- 
tus must be left to the judgment of the person conducting the 
test ; always keeping in mind the main object, i.e., to obtain 
authentic data. 

VI. See that the boiler is thoroughly heated before the trial to 
its usual working temperature. If the boiler is new and of a 

* These coals are selected because they are about the only coals which possess 
the essentials of excellence of quality, adaptability to various kinds of furnaces, 
grates, boilers, and methods of firing, and wide distribution and general accessi- 
bility in the markets. See various appendices in Vol. XXI, Transactions 
A. S. M. E. 



49 8 EXPERIMENTAL ENGINEERING. [§ 375- 

form provided with a brick setting, it should be in regular use 
at least a week before the trial, so as to dry and heat the walls. 
If it has been laid off and become cold, it should be worked 
before the trial until the walls are well heated. 

VII. The hoiler and connections should be proved to be free from 
leaks before beginning a test, and all water connections, includ- 
ing blow and extra feed pipes, should be disconnected, stopped 
with blank flanges, or bled through special openings beyond the 
valves, except the particular pipe through which water is to be 
fed to the boiler during the trial. During the test the blow-off 
and feed pipes should remain exposed to view. 

If an injector is used, it should receive steam directly through 
a felted pipe from the boiler being tested.* 

If the water is metered after it passes the injector, its tem- 
perature should be taken at the point where it leaves the injector. 
If the quantity is determined before it goes to the injector the 
temperature should be determined on the suction side of the 
injector, and if no change of temperature occurs other than that 
due to the injector, the temperature thus determined is properly 
that of the feed-water. When the temperature changes between 
the injector and the boiler, as by the use of a heater or by radi- 
ation, the temperature at which the water enters and leaves the 
injector and that at which it enters the boiler should all be 
taken. In that case the weight to be used is that of the water 
leaving the injector, computed from the heat units if not 
directly measured, and the temperature, that of the water 
entering the boiler. 

Let w = weight of water entering the injector. 
x = " " steam " 
h 1 — heat units per pound of water entering injector. 



\ = " " " " " steam 


it 


A 3 = " " " " " water leaving 


iC 


Then, w + x = weight of water leaving injector. 




h 3 — h } 
x = W j 1 — - T L - 
K — K 





* In feeding a boiler undergoing test with an injector taking steam from another 
boiler, or from the main steam pipe from several boilers, the evaporative results 
may be modified by a difference in the quality of the steam from such source 
compared with that supplied by the boiler being tested, and in some cases the 
connection to the injector may act as a drip for the main steam pipe. If it is 
known that the steam from the main pipe is of the same pressure and quality as 
that furnished by the boiler undergoing the test, the steam may be taken from 
such main pipe. 



§ 375-] TESTING STEAM-BOILERS. 499 

See that the steam main is so arranged that water of con- 
densation cannot run back into the boiler. 

VIII. Duration of the Test. — For tests made to ascertain either 
the maximum economy or the maximum capacity of a boiler, irre- 
spective of the particular class of service for which it is regularly 
used, the duration should be at least 10 hours of continuous run- 
ning. If the rate of combustion exceeds 25 pounds of coal per 
square foot of grate surface per hour, it may be stopped when a to- 
tal of 250 pounds of coal has been burned per square foot of grate. 

In cases where the service requires continuous running for 
th,e whole 24 hours of the day, with shifts of firemen a number 
of times during that period, it is well to continue the test for at 
least 24 hours. 

When it is desired to ascertain the performance under the 
working conditions of practical running, whether the boiler be 
regularly in use 24 hours a day or only a certain number of 
hours out of each 24, the fires being banked the balance of the 
time, the duration should not be less than 24 hours. 

IX. Starting and Stopping a Test. — The conditions of the boiler 
and furnace in all respects should be, as nearly as possible, the 
same at the end as at the beginning of the test. The steam 
pressure should be the same ; the water level the same ; the fire 
upon the grates should be the same in quantity and condition ; 
and the walls, flues, etc., should be of the same temperature. 
Two methods of obtaining the desired equality of conditions of 
the fire may be used, viz. : those which were called in the Code 
of 1885 " the standard method " and " the alternate method," 
the latter being employed where it is inconvenient to make 
use of the standard method.* 

X. Standard Method of Starting and Stopping a Test. — Steam 
being raised to the working pressure, remove rapidly all 
the fire from the grate, close the damper, clean the ash pit, 
and as quickly as possible start a new fire with weighed 
wood and coal, noting the time and the water level t while 

* The Committee concludes that it is best to retain the designations "stand- 
ard" and " alternate," since they have become widely known and established in 
the minds of engineers and in the reprints of the Code of 1885. Many engineers 
prefer the " alternate" to the "standard " method on account of its being less 
liable to error due to cooling of the boiler at the beginning and end of a test. 

f The gauge-glass should not be blown out within an hour before the water 
level is taken at the beginning and end of a test, otherwise an error in the read- 
ing of the water level may be caused by a change in the temperature and density 
of the water in the pipe leading from the bottom of the glass into the boiler. 



500 EXPERIMENTAL ENGINEERING. [§ 375. 

the water is in a quiescent state, just before lighting the 
fire. 

At the end of the test remove the whole fire, which has 
been burned low, clean the grates and ash pit, and note the 
water level when the water is in a quiescent state, and 
record the time of hauling the fire. The water level should 
be as nearly as possible the same as at the beginning of the 
test. If it is not the same, a correction should be made by 
computation, and not by operating the puiLp after the test is 
completed. 

XI. Alternate Method of Starting and Stepping a Test. — The 
boiler being thoroughly heated by a preliminary run, the fires 
are to be burned low and well cleaned. Note the amount of 
coal left on the grate as nearly as it can be estimated ; note the 
pressure of steam and the water level. Note the time, and 
record it as the starting time. Fresh coal which has been 
weighed should now be fired. The ash pits should be thor- 
oughly cleaned at once after starting. Before the end of the 
test the fires should be burned low, just as before the start, and 
the fires cleaned in such a manner as to leave a bed of coal on 
the grates of the same depth, and in the same condition, as at 
the start. When this stage is reached, note the time and record 
it as the stopping time. The water level and steam pressures 
should previously be brought as nearly as possible to the same 
point as at the start. If the water level is not the same as at 
the start, a correction should be made by computation, and not 
by operating the pump after the test is completed. 

XII. Uniformity of Conditions. — In all trials made to ascertain 
maximum economy or capacity, the conditions should be main- 
tained uniformly constant. Arrangements should be made to 
dispose of the steam so that the rate of evaporation may be 
kept the same from beginning to end. This may be accom- 
plished in a single boiler by carrying the steam through a 
waste steam pipe, the discharge from which can be regulated as 
desired. In a battery of boilers, in which only one is tested, 
the draft may be regulated on the remaining boilers, leaving the 
test boiler to work under a constant rate of production. 

Uniformity of conditions should prevail as to the pressure of 
steam, the height of water, the rate of evaporation, the thickness 
of fire, the times of firing and quantity of coal fired at one time, 
and as to the intervals between the times of cleaning the fires. 



§ 375-1 TESTING STEAM-BOILERS. 5 01 

The method of firing to be carried on in such tests should be 
dictated by the expert or person in responsible charge of the 
test, and the method adopted should be adhered to by the fire- 
man throughout the test. 

XIII. Keeping the Records. — Take note of every event con* 
n?,cted with the progress of the trial, however unimportant it 
may appear. Record the time of every occurrence and the 
time of taking every weight and every observation. 

The coal should be weighed and delivered to the fireman in 
equal proportions, each sufficient for not more than one hour's 
run, and a fresh portion should not be delivered until the pre- 
vious one has all been fired. The time required to consume 
each portion should be noted, the time being recorded at the 
instant of firing the last of each portion. It is desirable that at 
the same time the amount of water fed into the boiler should be 
accurately noted and recorded, including the height of the 
water in the boiler, and the average pressure of steam and tem- 
perature of feed during the time. By thus recording the 
amount of water evaporated by successive portions of coal, the 
test may be divided into several periods if desired, and the de- 
gree of uniformity of combustion, evaporation, and economy 
analyzed for each period. In addition to these records of the 
coal and the feed water, half hourly observations should be made 
of the temperature of the feed water, of the flue gases, of the 
external air in the boiler-room, of the temperature of the fur- 
nace when a furnace pyrometer is used, also of the pressure of 
steam, and of the readings of the instruments for determining 
the moisture in the steam. A log should be kept on properly 
prepared blanks containing columns for record of the various 
observations. 

When the " standard method " of starting and stopping the 
test is used, the hourly rate of combustion and of evaporation 
and the horse-power should be computed from the records taken 
during the time when the fires are in active condition. This 
time is somewhat less than the actual time which elapses be- 
tween the beginning and end of the run. The loss of time due 
to kindling the fire at the beginning and burning it out at the 
and makes this course necessary. 

XIV. Quality of Steam. — The percentage of moisture in the 
steam should be determined by the use of either a throttling or 



502 • EXPERIMENTAL ENGINEERING. \% 37$.. 

a separating steam calorimeter. The sampling nozzle should 
be placed in the vertical steam pipe rising from the boiler. It 
should be made of J-inch pipe, and should extend across the 
diameter of the steam pipe to within half an inch of the oppo- 
site side, being closed at the end and perforated with not less 
than twenty |-inch holes equally distributed along and around 
its cylindrical surface, but none of these holes should be nearer 
than \ inch to the inner side of the steam pipe. The calorim 
eter and the pipe leading to it should be well covered with 
felting. Whenever the indications of the throttling or separat- 
ing calorimeter show that the percentage of moisture is irregu- 
lar, or occasionally in excess of three per cent., the results should 
be checked by a steam separator placed in the steam pipe as 
close to the boiler as convenient, with a calorimeter in the steam 
pipe just beyond the outlet from the separator. The drip from 
the separator should be caught and weighed, and the percent- 
age of moisture computed therefrom added to that shown by 
the calorimeter. (See Chapter XIII, page 438.) ) 

Superheating should be determined by means of a thermome- 
ter placed in a mercury well inserted in the steam pipe. The 
degree of superheating should be taken as the difference be- 
tween the reading of the thermometer for superheated steam 
and the readings of the same thermometer for saturated steam 
at the same pressure as determined by a special experiment, 
and not by reference to steam tables. 

For calculations relating to quality of steam and corrections 
for quality of steam, see Chapter XIII, pages 393 and 435. 

XV. Sampling the Coal and Determining its Moisture. — As 
each barrow load or fresh portion of coal is taken from the coal 
pile, a representative shovelful is selected from it and placed in 
a barrel or box in a cool place and kept until the end of the 
trial. The samples are then mixed and broken into pieces not 
exceeding one inch in diameter, and reduced by the process of 
repeated quartering and crushing until a final sample weighing 
about iiYe pounds is obtained, and the size of the larger pieces 
is such that they will pass through a sieve with J-inch meshes. 
From this sample two one-quart, air-tight glass preserving jars, 
or other air-tight vessels which will prevent the escape of moist- 
ure from the sample, are to be promptly filled, and these sam- 
ples are to be kept for subsequent determinations of moisture 
and of heating value and for chemical analyses. During the 






§ 375-] TESTING STEAM-BOILERS. 5°3 

process of quartering, when the sample has been reduced to 
about 100 pounds, a quarter to a half of it may be taken for an 
approximate determination of moisture. This may be made by 
placing it in a shallow iron pan, not over three inches deep, 
carefully weighing it, and setting the pan in the hottest place 
that can be found on the brickwork of the boiler setting or flues, 
keeping it there for at least 12 hours, and then weighing it. 
The determination of moisture thus made is believed to be ap- 
proximately accurate for anthracite and semi-bituminous coals, 
and also for Pittsburg or Youghiogheny coal ; but it cannot be 
relied upon for coals mined west of Pittsburg, or for other coals 
containing inherent moisture. For these latter coals it is impor- 
tant that a more accurate method be adopted. The method 
recommended by the Committee for all accurate tests, whatever 
the character of the coal, is described as follows : 

Take one of the samples contained in the glass jars, and 
subject it to a thorough air-drying, by spreading it in a thin layer 
and exposing it for several hours to the atmosphere of a warm 
room, weighing it before and after, thereby determining the quan- 
tity of surface moisture it contains. Then crush the whole of it by 
running it through an ordinary coffee mill adjusted so as to pro- 
duce somewhat coarse grains (less than T Vinch), thoroughly mix 
the crushed sample, select from it a portion of from 10 to 50 
grams, weigh it in a balance which will easily show a variation 
as small as 1 part in 1,000, and dry it in an air or sand bath at 
a temperature between 240 and 280 degrees Fahr. for one hour. 
Weigh it and record the loss, then heat and weigh it again 
repeatedly, at intervals of an hour or less, until the minimum 
weight has been reached and the weight begins to increase by 
oxidation of a portion of the coal. The difference between the 
original and the minimum weight is taken as the moisture in the 
air-dried coal. This moisture test should preferably be made 
on duplicate samples, and the results should agree within 0.3 
to 0.4 of one per cent., the mean of the two determinations being 
taken as the correct result. The sum of the percentage of 
moisture thus found and the percentage of surface moisture 
previously determined is the total moisture. 

XVI. Treatment of Ashes and Refuse. — The ashes and refuse 
are to be weighed in a dry state. If it is found desirable to* 
show the principal characteristics of the ash, a sample should 
be subjected to a proximate analysis and the actual amount- 



504 



EXPERIMEN TA L ENG I NEE RING 



E§ 375- 



of incombustible material determined. For elaborate trials a 
complete analysis of the ash. and refuse should be made. 

XVII. Calorific Tests and Analysis of Coal.— The quality of the 
fuel should be determined either by heat test or by analysis, or 
by both. 

The rational method of determining the total heat of combus- 
tion is to burn the sample of coal in an atmosphere of oxygen 
gas, the coal to be sampled as directed in Article XV. of this 
code. (See Chapter XIV.) 

The chemical analysis of the coal should be made only by an 
expert chemist. The total heat of combustion computed from 
the results of the ultimate analysis may be obtained by the 
use of Dulong's formula (with constants modified by recent 



determinations), viz. : 14,600 C + 62,000 



(*-D 



+ 4000 s, 



in which C, H, 0, and S refer to the proportions of carbon, hy- 
drogen, oxygen, and sulphur respectively, as determined by the 
ultimate analysis.* 

It is desirable that a proximate analysis should be made, 
thereby determining the relative proportions of volatile matter 
and fixed carbon. These proportions furnish an indication of 
the leading characteristics of the fuel, and serve to fix the 
class to which it belongs. (Page 470.) As an additional 
indication of the characteristics of the fuel, the specific gravity 
should be determined. 

XVIII. Analysis of Flue Gases. — The analysis of the flue gases 
is an especially valuable method of determining the relative 
value of different methods of firing, or of different kinds of fur- 
naces. In making these analyses great care should be taken to 
procure average samples — since the composition is apt to vary 
at different points of the flue pages 475 to 492). The com- 
position is also apt to vary from minute to minute, and for this 
reason the drawings of gas should last a considerable period of 
time. Where complete determinations are desired, the analyses 
should be intrusted to an expert chemist. For approximate 
determinations the Orsat t or the Hempel J apparatus may be 
used by the engineer. (See pages 481 and 483.) 

* Favre and Silberraan give 14,544 B.T.U. per pound carbon ; Berthelot 14,64V 
B.T.U. Favre and Silberman give 62,032 B.T.U. per pound hydrogen ; Thomseu 
61,816 B.T.U. 

+ See R. S. Hale's paper on " Flue Gas Analysis," Transactions, vol xviil., p. 901. 

X See Hempel's " Methods of Gas Analysis " (Macmillan & Co.). 



§ 375-] TESTING STEAM-BOILERS. 505 

For the continuous indication of the amount of carbonic acid 
present in the flue gases, an instrument may be employed which 
shows the weight of the sample of gas passing through it. 

XIX. Smoke Observations. — It is desirable to have a uni- 
form system of determining and recording the quantity of smoke 
produced where bituminous coal is used. The system com- 
monly employed is to express the degree of smokiness by means 
of percentages dependent upon the judgment of the observer. 
The Committee does not place much value upon a percentage 
method, because it depends so largely upon the personal ele- 
ment, but if this method is used, it is desirable that, so far as 
possible, a definition be given in explicit terms as to the basis 
and method employed in arriving at the percentage. The actual 
measurement of a sample of soot and smoke by some form of 
meter is to be preferred. (See Appendices XXXIV. and XXXV.) 

XX. Miscellaneous. — In tests for purposes of scientific re- 
search, in which the determination of all the variables entering 
into the test is desired, certain observations should be made 
which are in general unnecessary for ordinary tests. These are 
the measurement of the air supply, the determination of its 
contained moisture, the determination of the amount of heat 
lost by radiation, of the amount of infiltration of air through 
the setting, and (by condensation of all the steam made by the 
boiler) of the total heat imparted to the water. 

As these determinations are rarely undertaken, it is not 
deemed advisable to give directions for making them. 

XXI. Calculations of Efficiency. — Two methods of defining and 
calculating the efficiency of a boiler are recommended. They are : 

1 -n«? • <!^i 1 -i Heat absorbed per lb. combustible 

1. Efficiency of the boiler = ^—, — ^ = f— ^ , -^ — 

J Calorific value 01 1 lb. combustible 

n -n/v. • £ j-i i .i i , Heat absorbed per lb. coal 

2. Efficiency of the boiler and grate = ~-^ — ^ , \ „ „ , 

Calorific value of 1 lb. coal 

The first of these is sometimes called the efficiency based on 
combustible, and the second the efficiency based on coal. The 
first is recommended as a standard of comparison for all tests, 
and this is the one which is understood to be referred to when 
the word " efficiency " alone is used without qualification. The 
second, however, should be included in a report of a test, to- 
gether with the first, whenever the object of the test is to deter- 
mine the efficiency of the boiler and furnace together with the 



506 



EXPERIMENTAL ENGINEERING. 



\\ 375- 



grate (or mechanical stoker), or to compare different furnaces, 
grates, fuels, or methods of firing. 

The heat absorbed per pound of combustible (or per pound 
coal) is to be calculated by multiplying the equivalent evapora- 
tion from and at 212 degrees per pound combustible Cor coal) by 
965.7. 

XXII. The Heat Balance. — An approximate " heat balance," or 
statement of the distribution of the heating value of the coal 
among the several items of heat utilized and. heat lost may be 
included in the report of a test when analyses of the fuel and of 
the chimney gases have been made. It should be reported in 
the following form : 

Heat Balance, or Distribution of the Heating Value of the Combustible. 
Total Heat Value of 1 lb. of Combustible B. T. U. 



Heat absorbed by the boiler = evaporation from and at 212 

degrees per pound of combustible x 965.7. 
Loss due to moisture in coal = per cent, of moisture referred 

to combustible -*- 100 x [(212 - t) + 966 + 0.48 (T — 

212)] (t =r. temperature of air in the boiler-room, T = 

that of the flue gases) 
Loss due to moisture formed by the burning of hydrogen 

= per cent, of hydrogen to combustible -r- 100 x 9 x 

[ (212 - t) + 966 + 0.48 (T - 212)]. 
Loss due to heat carried away in the dry chimney gases = 

weight of gas per pound of combustible x 0.24 x {T — t). 

CO 
5.f Loss due to incomplete combustion of carbon = 



i. 



per cent. C in combustible 
100 



C0 2 + CO 



10,150. 



6. Lose due to unconsumed hydrogen and hydrocarbons, to 
heating the moisture in the air, to radiation, and unac- 
counted for. (Some of these losses may be separately 
itemized if data are obtained from which they may be 
calculated.) 

Totals 



B. T. U 



Per Cent 



100.00 



*The weight of gas per pound of carbon burned may be calculated from the gas analyses as 
follows : 

Dry gas per pound carbon = " C0 * * ® ° + 7 (CO + N) , in which CO„, CO, O, and N are the 

3 (COj + CO) 
percentages by volume of the several gases. As the sampling and analyses of the gases in the 
present state of the art are liable to considerable errors, the result of this calculation is usually 
only an approximate one. The heat balance itself is also only approximate for this reason, as well 
as for the fact that it is not possible to determine accurately the percentage of unburned hydrogen 
or hydrocarbons in the flue gases. 

The weight of dry gas per pound of combustible is found by multiptying the dry gas per pound 
of carbon by the percentage of carbon in the combustible, and dividing by 100. 

t C0 2 and CO are respectively the percentage by volume of carbonic acid and carbonic oxide in 
the flue gases. The quantity 10,150 = Number of heat units generated by burning to carbonic 
acid one pound of carbon contained in carbonic oxide. 

XXIII. Report of the Trial. — The data and results should be 
reported in the manner given in either one of the two following 



§ 375-] TESTING STEAM-BOILERS. 



507 



tables, omitting lines where the tests have not been made as 
elaborately as provided for in such tables. Additional lines may 
be added for data relating to the specific object of the test. The. 
extra lines should be classified under the headings provided in 
the tables, and numbered as per preceding line, with sub letters 
a, b, etc. The Short Form of Report, Table No. 2, is recom- 
mended for commercial tests and as a convenient form of 
abridging the longer form for publication when saving of space 
is desirable. f For elaborate trials, it is recommended that the 
full log of the trial be shown graphically, by means of a chart, 
(See page 495.) 

TABLE NO. 1. 
Data and Results of Evaporative Test, 

Arranged in accordance with the Complete Form advised by the Boiler Test 
Committee of the American Society of Mechanical Engineers. Code of 1899. 

Made by of boiler at to 

determine 



Principal conditions governing the trial 



Kind of fuel* 

Kind of furnace 

State of the weather. 



Method of starting and stopping the test (" standard" or " alternate," Art. X. 
and XI. , Code) 

1. Date of trial 

2. Duration of trial hourt. 

Dimensions and Proportions. 

(A complete description of the boiler, and drawings of the same if of unusual 
type, should be given on an annexed sheet. (See Appendix X.) 

3. Grate surface . . .width length area 

4. Height of f urnace , 

5. Approximate width of air spaces in grate 

6. Proportion of air space to whole grate surface 

7. Water -heating surface 

8. Superheating surface 

9. Ratio of water-heating surface to grate surface 

10. Ratio of minimum draft area to grate surface 

* The items printed in italics correspond to the items in the " Short Form of Code. 
t Also see short form on page 513, used in Cornell University. 



sq. ft. 


ins. 


in. 


per cent. 


sq. ft. 


a 


— tol. 


1 to — 



508 EXPERIMENTAL ENGINEERING. [§ 375- 

Average Pressure*. 

11. Steam pressure by gauge lbs. per sq.in, 

12. Force of draft between damper and boiler . ins. of water 

13. Force of draft in furnace . . " " 

14. Force of draft or blast in ashpit «« «' 

Average Temperatures. 

15. Of external air , deg". 

16. Of fireroom •« 

17. Of steam " 

18. Of feed water entering beater. " 

19. Of feed water entering economizer •' 

20. Of feed water entering boiler ' ' 

21. Of escaping gases from boiler •• 

22. Of escaping gases from economizer *• 



Fuel. 

23. Size and condition 

24. Weight of wood used in lighting fire lbs. 

25. Weight of coal as fired * " 

26. Percentage of moisture in coal \ per cent. 

27. Total weight of dry coal consumed lbs. 

28. Total ash and refuse " 

29. Quality of ash and refuse 

30. Total combustible consumed lbs. 

31. Percentage of ash and refuse in dry coal per cent. 



Proximate Analysis of Coal. 

(App. XII.) 

Of Coal. Of Combustible. 

32. Fixed carbon per cent. per cent. 

33. Volatile matter " " 

34. Moisture " 

35. Ash " 

100 per cent. 100 per cent. 

36. Sulphur, separately determined " " 



* Including equivalent of wood used in lighting the fire, not including unburnt coal withdrawn 
from furnace at times of cleaning and at end of test. One pound of wood is taken to be equal to 
0.4 pound of coal, or, in case greater accuracy is desired, as having a heat value equivalent to the 
evaporation of 6 pounds of water from and at 212 degrees per pound. (6 x 965.7 = 5,794 B. T. U.) 
The term "as fired " means il its actual condition, including moisture. 

t This i8 the total moisture in the coal as found by drying it artificially, as described in Art, 
XV. of Code. 



§ 375-1 TESTING STEAM-BOILERS. 5°9 

Ultimate Analysis of Dry Coal. 

(Art. XVII., Code.) 

Of Coal. Of Combustible. 

37. Carbon (C) per cent. per cent. 

38. Hydrogen (H) 

39. Oxygen(O) 

40. Nitrogen (N) 

41. Sulphur (S) " " 

43. Ash " 

100 per cent. 100 per cent. 

43. Moisture in sample of coal as received " •' 

Analysis of Ash and Refute. 

44. Carbon per cent. 

45. Earthy matter " 

Fuel per Hour. 

46. Dry coal consumed per hour lbs. 

47. Combustible consumed per hour " 

48. Dry coal per square foot of grate surf ace per hour " 

49. Combustible per square foot of water-heating surface per hour. " 

Calorific Value of Fuel. 
(Art. XVII., Code.) 

50. Calorific value by oxygen calorimeter, per lb. of dry coal B.T.U. 

51. Calorific value by oxygen calorimeter, per lb. of combustible " 

52. Calorific value by analysis, per lb. of dry coal * , • " 

53. Calorific value by analysis, per lb. of combustible *' 

Quality of Steam. 
(App. XV. to XIX.) 

54. Percentage of moisture in steam per cent. 

55. Number of degrees of superheating deg. 

56. Quality of steam (dry steam = unity). (For exact determina- 

tion of the factor of correction for quality of steam see Ap- 
pendix XVIII.) 

Water. 
(App. I., IV., VII., VIII.) 

57. Total weight of water fed to boiler f lbs. 

58. Equivalent water fed to boiler from and at 212 degrees. ...... " 

59. Water actually evaporated, corrected for quality of steam " 

* See formula for calorific value under Article XVII. of Code. 

t Corrected for inequality of water level and of steam pressure at beginning and end of test. 



5io 



EXPERIMENTAL ENGINEERING. 



60. Factor of evaporation * 

61. Equivalent water evaporated into dry steam from and at 212 

degrees, f (Item 59 x Item 60.) 

Water per Hour. 

62. Water evaporated per hour, corrected for quality of steam 

63. Equivalent evaporation per hour from and at 212 degrees \ 

64. Equivalent evaporation per hour from and at 212 degrees per 

square foot of water-heating surface f 



Horse-Power. 

65. Horse-power developed. (34| lbs. of water evaporated per hour 

into dry steam from and at 212 degrees, equals one horse- 
power) t H. P. 

66. Builders' rated horse-power " 

67. Percentage of builders' rated horse-power developed per cent. 



Economic Results. 

68. Water apparently evaporated under actual conditions per pound 

of coal as fired. {Item 57 -f- Item 25. ) 

69. Equivalent evaporation from and at 212 degrees per pound of 

coal as fired, f {Item 61 -r- Item 25.) 

70. Equivalent evaporation from and at 212 degrees per pound of dry 

coal. \ {Item 61 -f- Item 27.) 

71. Equivalent evaporation from and at 212 degrees per pound of 

combustible, f {Item 61 -f- Item 30.) 

(If the equivalent evaporation, Items 69, 70, and 71, is not cor- 
rected for the quality of steam, the fact should be stated). 



lbs. 



Efficiency. 
(Art. XXL, Code.) 

72. Efficiency of the boiler ; heat absorbed by the boiler per lb. of com- 

bustible divided by the heat value of one lb. of combustible § . . . . per cent. 

73. Efficiency of boiler, including the grate; heat absorbed by the 

boiler, per lb. of dry coal, divided by the heat value of one lb. of 

dry coal " 

* Factor of evaporation = ~ , in which H and h are respectively the total heat in steam of 

the average observed pressure, and in water of the average observed temperature of the feed. 

t The symbol " U. E." meaning "Units of Evaporation," may be conveniently substituted for 
the expression "Equivalent water evaporated into dry steam from and at 212 degrees," its defini- 
tion being given in a foot-note. 

X Held to be the equivalent of £0 lbs. of water per hour evaporated from 100 degrees Fahr. into 
dry steam at ?0 lbs. gauge pressure. (See page 494.) 

§ In all cases where the word combustible is used, it means the coal without moisture and ash, 
but including all other constituents. It is the same as what is called in Europe •• coal dry and free 
from ash." 



§ 375-] TESTING STEAM-BOILERS. 511 

Cost of Evaporation. 

74. Cost of coal per ton of lbs. delivered in boiler room $ 

75. Cost of fuel for evaporating 1,000 lbs. of water under observed 

conditions <$ 

76. Cost of fuel used for evaporating 1,000 lbs. of water from and at 

212 degrees $ 

Smoke Observations. 
(App. XXXIV. and XXXV.) 

77. Percentage of smoke as observed per cent. 

78. Weight of soot per hour obtained from smoke meter ounces. 

79. Volume of soot per hour obtained from smoke meter cub. in. 

Methods of Firing. 

80. Kind of firing (spreading, alternate, or coking) 

81. Average thickness of fire 

82. Average intervals between firings for each furnace during time 

when fires are in normal condition ... 

83. Average interval between times of levelling or breaking up. . . . 

Analyses of the Dry Gases. 

84. Carbon dioxide (C0 2 ) per cent. 

85. Oxygen (O) 

86. Carbon monoxide (CO) •' 

87. Hydrogen and hydrocarbons " 

88. Nitrogen (by difference) (N) " 



100 per cent. 
TABLE NO. 2. 

Data and Results op Evaporative Test, 
Arranged in accordance with the Short Form advised by the Boiler Test Com- 
mittee of the American Society of Mechanical Engineers. Code of 1899. 

Made by on boiler, at to 

determine 

Kind of fuel 

Kind of furnace 

Method of starting and stopping the test ("standard" or " alternate/' Art. X. 

and XI., Code) 

Grate surface , sq. ft. 

Water-heating surface " 

Superheating surface " 

Total Quantities. 

1. Date of trial 

2. Duration of trial hours. 

3. Weight of coal as fired * ; lbs. 

4. Percentage of moisture in coal * per cent. 

5. Total weight of dry coal consumed lbs. 

6. Total ash and refuse " 

7. Percentage of ash and refuse in dry coal per cent. 

* See foot-notes of Complete Form. 



5'2 EXPERIMENTAL ENGINEERING. [§ 375. 

8. Total weight of water fed to the boiler *. * . „ lbs. 

9. Water actually evaporated, corrected for moisture or super- 

heat in steam 

10. Equivalent water evaporated into dry steam from and at 212 

degrees* '•' 

Hourly Quantities. 

11. Dry coal consumed per hour lbs. 

12. Dry coal per square foot of grate surface per hour ,s 

13. Water evaporated per hour corrected for quality of steam. ... " 

14. Equivalent evaporation per hour from and at 212 degrees *. , . " 

15. Equivalent evaporation per hour from and at 212 degrees per 

square foot of water-heating surface * " 

Average Pressures, Temperatures, etc. 

16. Steam pressure by gauge lbs. per sq. in. 

17. Temperature of feed water entering boiler deg. 

18. Temperature of escaping gases from boiler " 

19. Force of draft between damper and boiler ins. of water. 

20. Percentage of moisture in steam, or number of degrees of 

superheating per cent, or deg. 

Horse-Power. 

21. Horse-power developed (Item 14 -s- 34£) * H. P. 

22. Builders' rated horse-power " 

23. Percentage of builders' rated horse-power developed per cent. 

Economic Results. 

24. Water apparently evaporated under actual conditions per 

pound of coal as fired. (Item 8 -4- Item 3) lbs. 

25. Equivalent evaporation from and at 212 degrees per pound of 

coal as fired.* (Item 10 -4- Item 3) 

26. Equivalent evaporation from and at 212 degrees per pound of 

dry coal.* (Item 10 -4- Item 5) " 

27. Equivalent evaporation from and at 212 degrees per pound of 

combustible.* [Item 10 -4- (Item 5 — Item 6)J M 

(If Items 25, 26, and 27 are not corrected for quality of steam, 
the fact should be stated.) 

Efficiency. 

28. Calorific value of the dry coal per pound B. T. U. 

29. Calorific value of the combustible per pound , 

30. Efficiency of boiler (based on combustible) * per cent. 

31. Efficiency of boiler, including grate (based on dry coal) 

Cost of Evaporation. 

32. Cost of coal per ton of lbs. delivered in boiler-room $ 

33. Cost of coal required for evaporating 1,000 pounds of water 

from and at 212 degrees % 

*See foot-notes of Complete Form. 



§ 376-] 



METHODS OF TESTING STEAM-BOILERS. 



513 



276. CONDENSED REPORT OF BOILER-TEST. 

(Sibley College, Cornell University.) 
Log of Boiler-trial. 



Mpde at. 

Date 

Fireman 



::; 89 :: B H ::::::: 

Report of Boiler-test. 



Made by. . 
Kind of Boiler, 



N. Y. 

Manufactured by. 



189. 



Duration of Trial Hours. 

Grate-surf., length ft., 

width ft , Sq. ft. 

Water-heating surface " 

Superheating surface " 

Area for draught (calorimeter). " 

Area, chimney " 

Height, chimney Ft. 

Ratio heating to grate surface 

Ratio air-space to grate-surface 

Barometer Inches mercury. 

Steam-gauge Pounds. 

Draught-gauge Inches water, 

Absolute steam-pressure Pounds, 

External air Degrees F, 

Boiler-room " 

Flue 

Furnace " 

Feed-water " 

Steam " 

Total coal consumed Pounds. 

Moisture in coal Per cent. 

Dry coal consu med Pounds. 

Total refuse, dry " 

Total refuse, dry Percent, 

Total combustible Pounds, 

Dry coal per hour " 

Combustible per hour " 

Dry coal per square foot of 

grate " 

Combustible per square foot 

of grate " 

Dry coal per square foot of 

grate Heating-surface, 

Combustible per square foot of 

grate Heating-surface. 

Quality of steam Percent, 

Superheat Degrees, 

Total weight water used .... Pounds, 
(by meter)... Cu. ft. 

Total evap. , dry steam Pounds. 

Factor of evaporation ' 

Total from and at 212 .... Pounds. 



2X 



Amount used Pounds. 

Evaporated, dry steam " 

Evap. from and at 212 " 

Per Pound of Fuel. 

Actual Pounds. 

Equiv. from and at 212 " 

Per Pound of Combustible. 

Actual Pounds. 

Equiv. from and at 212 " 

Per Sq. Ft. Heating-surface per Hr. 

Actual Pounds. 

Equiv. from and at 212 " 

From ioo° F. to 70 Pounds by Gauge. 

Per Pound of Fuel Pounds. 

Per Pound of Combustible. . . " 
Per |-pound of Fuel ,; 

Per Square Foot of Grate. 

Actual, from feed-water tem- 
perature Pounds. 

Equiv. from and at 212 " 

Per Sq. Ft. of Water-heating Surface. 

Actual Pounds. 

Equiv. from and at 212 " 

Per Sq. Ft. of Least Draught-area. 

Actual Pounds. 

Equiv. from and at 212 li 

* On basis 34^ lbs. equiv. evap. 

per hour H. P. 

Builders' rating " 

Ratio of commercial to builders' rat- 
ing 

Heat generated per hour. . . B. T. U. 

Heat absorbed per hour " 

Efficiency of boiler Per cent. 

Efficiency of furnace , " 



Note. — Actual evaporation signifies the evaporation from feed-water temperature to dry 
m at eauee-pressure. It is apparent evaporation corrected for calorimeter-determination 



steam at gauge-pressui 

* Standard Commercial H. 



pparent 
P. 



.514 EXPERIMENTAL ENGINEERING. [§ 377- 

377. Abbreviated Directions for Boiler-testing. — Ap- 
paratus. — As in standard tests : tanks and scales for weighing 
water; meter for measuring water; apparatus for flue-gas 
analysis ; barometer and pyrometer. 

Directions. — Calibrate all apparatus, meters, scales, ther- 
mometers, and gauges ; arrange throttling or separator calo- 
rimeter to obtain quality of steam delivered. Note condition 
of Boiler and Furnace Rules, VII-IX. Start and close the 
test either by standard or alternative method, Rules X and XL 
During test proceed as in Rules XIII and XIV. Continue 
the test as long as time will permit, at least four hours, taking 
simultaneous observations each 15 minutes at a signal given 
by a whistle ; keep record so that coal and water consumption 
can be computed for each hour. 

Put IOO pounds of coal in a box and dry in a hot place for 
24 hours ; if ashes are damp from use of a steam-blower, dry a 
sample of 100 pounds in same manner. In general, ashes may 
be removed at once and weighed. 

Report and Computation. — Make report on standard forms 
submitted and compute the required quantities. Submit with 
report a graphical log, in which time is taken as abscissa, and 
the various observed quantities as ordinates. 

Revised Code for Boiler-testing. — At the meeting of the 
American Society of Mechanical Engineers in December, 
1899, a revised code for boiler-testing was presented before 
the society by a special committee appointed for that pur- 
pose. The new code is given in the Appendix to this volume ; 
it differs from the old one principally in the use of improved 
methods. 









CHAPTER XVI. 



THE STEAM-ENGINE INDICATOR. 



378. Uses of the Steam-engine Indicator. — The steam- 
engine indicator is an instrument for drawing a diagram on 
paper which shall accurately represent the various changes of 
pressure on one side of the piston of the steam-engine during 
both the forward and return stroke. 




Fig 226. — The Indicator-diagram. 

The general form of the indicator-diagram is shown in Fig. 
226; the ordinates of the diagram, measured from the line 
GGj are proportional to the pressure per square inch above the 
atmosphere ; measured from the line HH, are proportional to 
the absolute pressure per square inch acting on the piston. 
The abscissa corresponding to any ordinate is proportional to 
the distance moved by the piston. ABCDE is the line drawn 
during the forward stroke of the engine, EFA that drawn dur- 
ing the return stroke. The ordinates to the line ABCDE rep- 
resent the pressures acting to move the piston forward ; those 
to the line EFA represent the pressures acting to retard or 

515 



5 16 EXPERIMENTAL ENGINEERING. [§ 379- 

stop the motion of the piston on its back stroke. The ordi- 
nates intercepted between the lines represent the effective 
pressure acting to urge the piston forward. Since the abscissae 
of the diagram are proportional to the space passed through 
by the piston, and the intercepted ordinate to the effective 
pressure acting on the piston, the area of the diagram must be 
proportional to the work done by the steam on one side of the 
piston, acting on a unit of area and during both forward and 
return stroke. (See Article 21, page 21.) 

From this diagram can be obtained, by processes to be ex- 
plained later: I. The quantity of power developed in the 
cylinder, and the quantity lost in various ways, — by wire-draw- 
ing, by back pressure, by premature release, by mal-adjustment 
of valves, leakage, etc. 

2. The redistribution of horizontal pressures at the crank- 
pin, through the momentum and inertia of the reciprocating 
parts, and the angular distribution of the tangential component 
of the horizontal pressure ; in other words, the rotative effect 
around the path of the crank. 

3. Taken in combination with measurements of feed-water 
or of the exhaust steam, with the amount and temperatures of 
condensing water, the" indicator furnishes opportunities for 
measuring the heat losses which occur at different points 
during the stroke. 

4. The indicator-diagram also shows the position of the 
piston at times when the valve-motion opens or closes the 
steam and exhaust ports of the engine. It also furnishes in- 
formation regarding the general condition of the engine, and 
the arrangement of the valves, adequacy of the ports and pas- 
sages, and of the steam or the exhaust pipes. 

379. Indicated and Dynamometric Power. — The steanu 
engine indicator is used in all steam-engine tests to measure 
the force of the steam acting on a unit of area of the piston. A 
dynamometer of the absorbing or transmission type (see pages 
235 to 2 50) is used to measure the work delivered by the steam- 
engine. The work of the engine is usually expressed in horse- 
power ; one horse-power being equivalent to 33,000 foot-pounds 



§ 38o.] 



THE STEAM-ENGINE INDICATOR. 



517 



per minute. The work shown by the steam-engine indicator- 
diagram is termed the Indicated horse-power (I.H.P.); that shown 
by the dynamometer, Dynamometric horse-power (D.H.P.). 

The mean effective pressure per unit of area acting on the 
piston is obtained from the indicator-diagram ; this quantity, 
multiplied by the area of the piston and the distance travelled 
by the piston in feet per minute, will give the work in foot- 
pounds. Thus let p equal the mean effective pressure, / the 
length of stroke of the engine in feet, n the number of revolu- 
tions, a the area of the piston in square inches. Then the 
work done per minute by the steam acting on one side of the 
piston, in horse-power, is 

plan ■— 33,000. 

380. Early Forms of the Steam-engine Indicator. — 

Watt and McNaught. — The steam-engine indicator was in- 
vented by James Watt, and was extensive- s 
ly used by him in perfecting his engine. 
The indicator of Watt,* as used in 18 14, 
consisted of a small steam-cylinder AA, 
as shown in Fig. 227, in which a piston 
was moved by the steam-pressure, against 
the resistance of a spring FC. The end 
of the piston-rod carried a pencil, which 
was made to press against a sheet of 
paper DD, moved backward and forward 
in conformity to the motion of the piston. 
By this method a diagram was produced 
similar to that shown in Fig. 227. 

McNaught's indicator, which succeeded 
that of Watt and was in general use until 
about i860, differed from the form used 
by Watt principally in the use of a verti- 
cal cylinder instead of the sliding panel, 
which was turned backward and forward 
on a vertical axis, in conformity to the motion of the piston. 




Fig. 227.— The Watt 
Indicator. 



See Thurston's Engine and Boiler Trials, page 130. 



5 i8 



EXPERIMENTAL ENGINEERING. 



[§38i. 



381. The Richards Indicator.* — The Richards indicator 
was invented by Professor C. B. Richards about i860 ; it con- 
tains every essential constructive feature found in recent indi- 
cators, and may be considered the prototype from which all 
other indicators differ simply in details of workmanship, form, 
and size of parts. 

The construction of this indicator is well shown in Fig. 228, 




Fig. 228. — The Richards Indicator. 

from which it is seen to consist of a steam-cylinder AA y in 
which is a piston B, connected by a rigid rod with the cap F. 
The movement of the piston is resisted by the spring CD in 
such a manner that its motion in either direction is proportional 
to the pressure. The motion of the piston-rod is transferred 
to a pencil at K, by links which are so arranged that the pencil 

* See the Richards Indicator, by C. B. Porter; New York, D. Van Nostrand. 



§ 332.] 



THE STEAM-ENGINE INDICATOR. 



519 



moves parallel to the piston B, but through a considerably 
greater range. The indicator-spring can be taken out by 
unscrewing the cap E, removing the top of the instrument and 
unscrewing the piston B, and another spring with a different 
tension can be substituted. The drum OR is made of light 
metal, mounted on a vertical axis, and provided with a spring 
arranged to resist rotation. The drum is connected to the cross- 
head or reducing motion by a cord, and is given a motion in one 
direction by the tension transmitted through the cord and in a 
reverse direction by the indicator drum-spring. The paper on 
which the diagram is to be drawn is wrapped smoothly around 
the drum OQ, being held in place by the clips PQ. The indicator 
is connected to the steam-cylinder by a pipe leading to the 
clearance-space of the engine; a cock, T, being screwed into this. 
pipe, and the indicator connected to the cock by the coupling U. 
382. The Thompson Indicator. — This indicator is shown 
in Figs. 229 and 230. It differs from the Richards indicator 





Fig. 2x9.— The Thompson Indicator. 



Fig. 230.— Section of Thompson 
Indicator. 



principally in the form of the parallel motion, form of indicator- 
spring, and details of workmanship. The parts of the instru- 



520 



EXPERIMEN TA L ENGINEERING. 



[§ 3»3< 



ment are much lighter, and it is better adapted for use on high- 
speed engines. 

The use is essentially the same as the Richards ; the method 
of changing springs should be thoroughly understood, and is as 
follows : Unscrew the milled-edged cap at the top of steam- 
cylinder ; then take out piston, with arm and connections ; dis- 
connect pencil-lever and piston by unscrewing the small milled- 
headed screw which connects them ; remove the spring from the 
piston, substitute the one desired, and put together in same 
manner, being careful, of course, to screw the spring up firmly 
against cap and well down to the piston-head. The method of 
changing springs is simple, easy, and convenient, and does not 
require the use of any wrench or pin of any kind. 

383. The Tabor Indicator. — The Tabor indicator, shown 
in Figs. 231 and 232, in the form now manufactured differs 
from other indicators principally in producing the parallel 




Fig. 231.— The Tabor Indicator. 



motion of the pencil by a pin moving in a peculiarly-shaped 
slot. It also differs in details of construction and in form 
of the indicator-spring; the pencil-point being arranged to 
move not only parallel to the piston, but uniformly five times 
a* fast as the piston at every part of the range. 



§ 384-] 



THE STEAM-ENGINE INDICATOR. 



521 




Fig. 232. — Section of Tabor Indicator. 



The method of changing springs in the Tabor indicator is as 
follows : Remove the cover of the 
cylinder, remove the screw beneath 
the piston, unscrew the piston from 
the spring and the spring from 
the cover, and replace the spring 
desired. When the lower end 
of the piston-rod is introduced 
into the square hole in the centre 
of the piston, care must be taken 
chat it sets fairly in the hole be- 
fore the screw is applied. Unless 
such care is observed, the corners 
may catch and cause derangement. 
The tension on the drum-spring 
may be varied by removing the 
paper drum, loosening the thumb-screw which encircles the 
central shaft, lifting the drum-carriage so as to clear the stop, 
and then winding the carriage in the direction desired. 

384. The Crosby Indicator. — The Crosby indicator as at 
present constructed is shown in Figs. 233 and 234. It differs 
from those already described in the form of piston- and drum- 
springs and in the arrangement for producing accurate parallel 
motion. 

The special directions for this instrument are given by the 
manufacturers as follows : 

To remove the piston, spring, etc., unscrew the cap, then, by 
the sleeve, lift all the connected parts free. This gives full 
access to the parts to clean and oil them. 

To detach the spring, unscrew the cap from spring-head, 
then unscrew piston-rod from swivel-head, then, with the hol- 
low slotted wrench, unscrew the piston-rod from the piston. 
To attach a spring, simply reverse this process. Before setting 
the foot of the spring unscrew G slightly, then, after the piston- 
rod has been firmly screwed down to its shoulder, set G up 
firmly against the bead, and thereby take up all lost motion. 

It is often desirable to change the position of the atmospheric 



522 



EXPERIMEN TA L ENGINEERING. 



[§ 384. 



line on the paper. This can easily be done by unscrewing the 
cap from the cylinder and raising the sleeve BB which carries 
the pencil-movement. Then turn the cap to the right or left, 




Fig. 233.— The Crosby Indicator. 



and the piston-rod will be screwed off or on the swivel E, and 
the position of the atmospheric line will be raised or lowered. 

Never remove the pins or screws from the joints K, I, L, M t 
but keep them well oiled with refined porpoise-jaw oil, which 
is furnished with each instrument. 

The tension on the drum-spring should be increased or 
diminished according to the speed at which the instrument is 
used, by means of the thumb-nut on top of the drum-spindle. 

Use a spring of such a number that the diagram will not be 



§385- 



THE STEAM-ENGINE INDICATOR. 



523 



over one and three-quarter inches high; as, for instance, a No. 
40 spring should not be used for pressures above 70 lbs. 




Fig. 234. — Section of the Crosby Indicator. 



385. Indicators with External Springs.— The Bachelder 
indicator, shown in Fig. 235, has a flat spring that is flexed over 
a movable fulcrum by the steam pressure acting on the piston. 
The scale of the spring is changed, through a limited range, by 
moving the fulcrum. This form is desirable when the spring 
is subjected to high temperatures; it is only open to the objec- 
tion that the scale may be somewhat unreliable due to an acci- 
dental motion of the fulcrum. 

An indicator with the spring entirely outside and above the 
indicator cylinder is shown in Fig. 236. For indicating gas- 



524 



EXPERIMEN TA L ENGINEERING, 



[§ 386. 



engines when the spring is exposed to a high temperature this 
form is desirable. That shown is a form of the Tabor. 





Fig. 235.— The Bachelder Indicator. 



Fig. 236. — Indicator with External 
Spring. 



386. Sundry Types of Indicators.— Many of the makers 
of indicators provide reducing-wheels which may be adapted to 




Fig. 237.— Indicator with Reducing-wheel. 

varying lengths of strokes either by changing gear-wheels in 
the train of gears, or by varying the diameter of the wheels driven 
by the cord from the cross-head. An indicator provided with 
one form of reducing-wheels is shown in Fig. 237. 



§ 38/.] 



THE STEAM-ENGINE INDICATOR. 



525 



In Figs. 238 and 238a are shown indicators with pencil-moving 
mechanism of different character from those described. In one 




Fig. 238.— The Straight-line Indicator. 



Fig. 238a.— The Perfection Indicator. 



case the pencil is directed in a straight line by a slotted guide- 
bar, in the other case it is made to move in a right line by a species 
of parallel motion links. 

387. Optical Indicators. — The ordinary steam-engine indi- 
cator is not adapted for a very high speed of rotation, because 
the inertia of the moving parts distorts the diagram. By arranging 
a mirror, which may be illuminated so as to be deflected in 
one direction by changes of pressure in the cylinder, and in a 
direction at right angles by the motion of the piston, the indi- 
cator diagram will be traced by a beam of light thrown on a 
ground-glass screen or on a sensitive plate in a camera. The 
form of the diagram may be studied by observing it on the ground 
plate, or it may be photographed and preserved. 

One form of this instrument is made by J. Carpentier of 
Paris, and is called the Manographie. Another form is made by 
the Elsassische Elektricitats-Werke, Strassburg, and is called 
the optical indicator. 

A perspective view and section of the Manographie is shown 
in Figs. 239 and 239a. A small mirror is located at A in the 



526 



^AL ENGINEERING. 




Fig 239- 



back part of the camera E. It is deflected in one direction by 
a small crank operated in unison with the engine piston by the 

revolving shaft. P, to 
1^1^^ which it is connected by 
the flexible shaft R, Fig. 
239; it is deflected in a 
direction at right angles 
against the resistance of 
a spring by the pressure 
from the engine cylinder 
acting through a pipe T 
upon a diaphragm di- 
rectly back of the mirror. 
The mirror is illuminated by light from a lamp at G which 

is reflected by the prism shown at H. The indicator diagram 

is traced on the screen D 

by the ray of light, and 

may be photographed by 

the use of a sensitive 

plate. This apparatus 

has been successfully 

used to take indicator 

diagrams of gas : engines 

when moving at the rate 

of 2000 revolutions per 

minute. 

388. Parts of the Steam-engine Indicator. — The parts of 

the steam-engine indicator are essentially as follows: 

1. The Steam-cylinder. — -This contains the piston, the indi- 
cator-spring, and attachments for the pencil mechanism. 

2. The Piston. — This is usually solid, with grooves or holes 
in its outer edge; it must move easily in the cylinder. When 
in use it must be lubricated with cylinder-oil of best quality. 

3. The Pencil Mechanism. — This receives the motion from 
the piston-rod, increases its amplitude, and transfers it to a 
pencil by means of guides or parallel-motion links, so that the 




Fig. 239a. 



§ 388.] 



THE STEAM-ENGINE INDICATOR. 



527 



pencil moves in a right line and usually four to six times the 
distance of the piston. The height of the atmospheric line, or 
line of no pressure, on the drum, can often be adjusted by 
means of a threaded sleeve fitting on the piston-rod. In the 
arc indicator the pencil swings in an arc of a circle. 

4. The Indicator- spring. — This is usually a helical spring; 
when in use it has one end screwed to the upper head of the 
cylinder, and the other screwed to the piston. To insure accu- 
rate results the spring must be accurate, and there must be no 
play or lost motion between the piston and the cylinder-head, 
and the spring must receive and deliver the force axially. The 
number of pounds pressure on the square inch required to move 
the pencil one inch is stamped on the spring, and the springs 
are designated by that number. It is essential to know the 
error, if any, in this number. A spring can be readily removed 
and another substituted when desired ; the maximum compres- 
sion probably should not exceed one third of an inch. 

The spring is in many respects the most important part of 
the indicator, as the form of the diagram is directly affected 
by any error. The following cuts show some of the principal 





Fig. 240. — Ckosby Spring. 



Fig. 241.— Tabor Spring. 



forms adopted by a few of the makers, and it may perhaps be 
sufficient to state that within the range of action of the indi- 
cator any of these forms can be made practically perfect. 



528 



EXPERIMENTAL ENGINEERING. 



[§ 339 





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§39°-] THE STEAM-ENGINE INDICATOR. 529 

The Bachelder indicator (see Fig. 238) is made with a flat 
spring, and to a certain extent the tension is regulated by 
changing its fulcrum. 

5. The Paper-drum, to which the card is attached, consists 
of a brass cylinder attached to a spindle which is connected 
to the drum-spring, the action of which has been described. 
The drum can be removed readily, and the tension on the 
spring changed at pleasure. Two clips or fingers serve to hold 
the paper in position. 

6. The Cord used, although not a part of the indicator, 
must be selected with great care; it must be of a character 
not to be stretched by the forces acting on the indicator. 
Steel wire is sometimes used for this purpose. Any variation 
in length of the connecting cord affects the abscissa in the 
diagram. 

7. The Reducing-motioits, also not a part of the indicator, 
must give an exact reproduction, on a smaller scale, of the 
motion of the piston ; otherwise the length of the indicator- 
diagram will either not be accurately reduced, or the events 
will not be properly timed. 

389. The table opposite gives the actual dimensions of the 
principal indicators described, as obtained by careful measure- 
ment of those owned by Sibley College. 

390. Reducing-motions for Indicators. — The maximum 
motion of the indicator-drum is usually less than four inches ; 
consequently it can seldom be connected directly to the cross- 
head of the engine, but must be connected to some apparatus 
which has a motion less in amplitude but corresponding exactly 
in all its phases to that of the cross-head. This apparatus is 
termed a reducing-motion. Since the horizontal components 
of the indicator-diagram and consequently its area and form 
depend upon the motion of the piston, it is evident that the 
accuracy of the diagram depends upon the accuracy of the 
reducing-motion. Various combinations of levers and pulleys 
have been used * for reducing-motions, a few of which will be 



See Thurston's Engine and Boiler Trials. 



530 



EXPERIMENTAL ENGINEERING. 



[§ 390. 



described. Several simple forms of reducing-motion are 
given here as suggestions, but it is expected that the student 
will devise other motions if required, and ascertain the amount 
of error, if any, in the motion used. 




FlG. 242. — The Simple Pendulum Reducing-motion. 

The cheaper and more easily arranged reducing-motion* 
consist usually of some form of swinging lever or pendulum 
(see Fig. 242) pivoted at one point, and connected at its 
lower end to the cross-head by a lever. The indicator-cord 
is attached to the swinging lever at some point having the 
proper motion. These motions never give an exact reproduc- 



§390.] 



THE STEAM-ENGINE INDICATOR. 



531 



tion of the motion of the piston ; but if the pendulum and 
cross-head are simultaneously at the centre of the stroke, the 
error is very small. 




Fig. 243.— The Brumbo Pulley. 



A form of the pendulum-motion, called the Brumbo pulley \ 
is frequently used as shown in Fig. 243. The pendulum is some- 
times modified, so that its lower end is pivoted directly to a 




Fig. 244 —The Pantograph. 

point in the cross-head, its upper half moving vertically in a 
swinging tube. The cord is attached to an arc on this tube as 
in Fig. 242. 



532 



EXPERIMENTAL ENGINEERING. 



L§ 391. 



The pantograph, or lazy-tongs, as shown in Fig. 244 with 
plan of method of attachment shown in Fig. 245, is a perfect 
reducing motion, but because of its numerous joints it is not 
adapted to high-speed engines. 




Fig. 245.— Method of Attaching the Pantograph. 

A form of pantograph with four joints only, shown in Fig. 
246, is much better adapted to high-speed engines than the one 
with more numerous joints shown above. 




Fig. 246.— Method of Using the Pantograph. 

Reducing-wheels. — Reducing wheels, which consist of a 
large and a small pulley (see Fig. 247) attached to the same 
axis, are extensively used by engineers. The method of attach- 
ing this reducing-motion to an engine is shown in Fig. 248. 

391. The Indicator-cord.— The indicator-cord should be as 
nearly as possible inextensible, since any stretch of the cord 
causes a corresponding error in the motion of the indicator- 
arum. As it is nearly impossible to secure a cord that will not 



§ 391-1 



THE STEAM-ENGINE INDICATOR. 



533 



stretch, it should be made as short as possible, and a fine wire of 
steel or iron or of hard-drawn brass should be used if practicable. 




Fig. 247.— Schaeffer and Budenberg Reducing-motiok. 




Fig. 248.— Webster and Perks Reducing-motion. 

The indicator-cord supplied by makers of indicators is a braided 
hard cotton cord, stretching but little under the required stress. 



5 34 EXPERIMENTAL ENGINEERING. [§ 392. 

If a "rig" is to be permanently erected, it is recommended that 
the motion be taken from a sliding bar attached to the cross- 
head and extending to or beyond the indicators. The angle 
of the cord with the path of motion of the cross-head should 
be as nearly constant as possible, since any variation in this 
angle will cause a distortion in the motion of the drum. 

In Figs. 243, 246, and 248 will -be seen devices to over- 
come the effect of angularity of the indicator-cord. 

The indicator-cord is usually hooked and unhooked into a 
loop in a cord fastened to the reducing-motion. A very con-, 
venient form for such a loop, and one that can readily be ad- 
justed, is shown in Fig. 249. The indicator-cord is usually 




Fig. 249.— The Loop. 

provided with a hook fastened as shown in Fig. 182, which is 
hooked when diagrams are needed into the loop attached to 
the reducing-motion. 

The author would strongly urge that the indicator-cord be 
arranged so as to avoid the necessity of frequent hooking and 
unhooking, thus throwing severe and unnecessary strains on 
the indicator-drum and cord : this can be done by connecting 
a point on the cord near the indicator with a spiral spring 
fastened to a fixed point in the line of the cord produced. This 
spring should be strong enough to keep the slack out of the cord. 
When it is desired to stop the motion, the drum-cord is pulled 
toward the reducing-motion to the extent of its travel, and 
held or tied until another diagram is needed. Some of the 
indicator-drums are provided with ratchets or detents that 
serve the same purpose. When several indicators are in 
use and simultaneous diagrams are required, a detent-motion 
worked by an electric current will prove very satisfactory. 
In case of compound engines when numerous indicators are re- 
quired these suggestions become of even greater importance. 

392. Standardization of the Indicator. — The accuracy of 



§393-] THE STEAM-ENGINE INDICATOR. 535 

the indicator-diagram depends upon the following features, all 
of which should be the subject of careful examination : 

(1) Uniformity of the indicator-spring. 

(2) Accuracy of the drum-motion. 

(3) Parallelism of the piston-movement to the cylinder. 

(4) Parallelism of the pencil-movement to the axis of the 
drum. 

(5) Friction of the piston and pencil-movements. 

(6) Lost motion. 

The calibration of these parts should be made as nearly as 
possible under the conditions of actual use and as described 
in the following articles. 

393. Calibration of the Indicator-spring.— The accuracy 
of the indicator-spring is only to be determined by comparison 
with standardized apparatus. This may be done as follows : 

Firstly : with the open mercury column. This can be done 
with steam only, as the leakage of water past the loosely-fitting 
piston would render it impossible to maintain the pressure. 
Insert the spring; see that the indicator is oiled and in good 
condition. Attach the indicator as previously explained for 
the calibration of steam-gauges, page 366 ; put paper on the 
drum; turn on steam-pressure until the instrument is warm; 
turn off the steam, and pressing the pencil lightly against the 
paper, turn the drum by hand, thus drawing the atmospheric 
line. Apply pressure by increments equal to one fifth that 
marked on the spring, keeping the motion continually upward, 
stopping only long enough to draw the line for the required 
pressure. Take ten increments first up then down ; the average 
position of any line will give the ordinate corresponding to 
that pressure ; the difference between any two lines (see Fig. 
250) will be twice the friction of indicator-piston at that point. 

Second : with the standard scales. This method was devised 
by Professor M. E. Cooley, of Ann Arbor. In this case the 
indicator is supported on a bracket above the platform of the 
scales. Force is applied to the indicator-piston by means of a 
rod which can be raised or lowered by turning a hand-wheel; 
this rod terminates above in a cap nicely fitted to the under 



53^ 



EXPERIMENTAL ENGINEERING. 



[§ 393- 



side of the piston, and below it rests on a pedestal standing on 
the platform of the scales. Any force applied to compress the 
spring is registered on the scale-beam. The reading of the 
scale-beam is that force acting on one-half square inch, as the 
piston is usually one-half square inch in area ; this is to be multi- 
plied by 2 to correspond with the reading given by the indica- 
tor-spring. The indicator can be heated by wrapping rubber 
tubing around the cylinder and passing steam through the tube. 





y TTp 


/ 


Down. 


feu 








55 
















b'yj 






45 










40 










S3 










SO 










25 










20 










Jb 








10 








b 










Tip. 


1) 

* 


Down. 

























































Fig 250. — iNDiCATOk-spRiNG Calibration. 



FORM FOR CALIBRATION OF INDICATOR-SPRING. 

By comparison with 

Make of indicator 

Mark and No. of spring 



Date. 



Observers 



No. 



Gauge. 


Actual 
Pressure. 




Ordinates. • 




Actual 
Pressure. 


Inches 


Lbs. 


Inches. 


Pounds. 


Up. 


Down. 


Mean. 



















Error. 
Per cent. 






§ 3941 



THE STEAM-ENGINE INDICATOR. 



537 



The indicator-springs should be calibrated as nearly as possi- 
ble under the conditions of actual use. The springs are elon- 
gated by increase in temperature and weakened because of that 
fact, so that the calibration of the spring cold will give results 
which differ by approximately 3 per cent, from the calibration when 
the spring is at a temperature approximating 212 , as has been 
proved by extended experiments.* 

Various forms of apparatus have been devised for the testing 
of indicator-springs both cold and hot. A simple device is shown 




Fig. 251.— Indicator-spring Testing Device. 



in Fig. 251 consisting of a cylinder, A, supported on a bracket 
above a pair of scales and fitted with a piston having an area of 
cross-section exactly the same as the indicator-piston. A rod 
from this piston extends downward on to a platform scale, as 
shown in the figure. The indicator is connected by suitable 



* Experiments, Marks and Barraclough, Vol. XV, Transactions A. S. M. E. 



538 



EXPERIMEN TA L ENGINEERING. 



[§ 395- 



piping to the upper end of the cylinder. The steam for the pur- 
pose of calibration is adjusted in pressure by a valve, E, before 
it enters the drum, B. The pressure in the steam in the drum 
is shown on the attached gauge. This steam-pressure exerts 
an upward pressure on the indicator-piston and a downward 
pressure on the piston in the cylinder, A, which latter, cor- 
rected for dead weight, is measured on the weighing-scales 
shown. 

A modification of this apparatus is shown in Fig. 252, 
which consists of a vessel, A, into which steam can be admitted 




p%= 



Fig. 252.— Indicatob.-spring Testing Apparatus. 



at any desired pressure. The pressure in the vessel acts on 
the piston, K, which is J square inch in area and may be 
measured by the attached scale-beam. The same pressure 
reacts on the indicator-piston. By taking simultaneous read- 
ings of the pressure on the piston, K, and on the indicator- 
piston, the calibration may be performed substantially as 
described. 

This apparatus has proved satisfactory after an extensive 
use. It can be purchased of Schaeffer & Budenberg of Brooklyn, 
N. Y. 



§ 395-] THE STEAM-ENGINE INDICATOR. 539 

394. Test for Parallelism of the Pencil-movement to the 
Axis of the Drum. — This is tested by removing the spring 
from the indicator, rotating the drum, and drawing an atmos- 
pheric line ; then hold the drum stationary in various positions 
and press the piston of the indicator upward throughout its 
full stroke, while the pencil is in contact with the paper. The 
lines thus drawn should be parallel to each other and perpen- 
dicular to the atmospheric line. 

Parallelism of the piston-movement to the cylinder axis is 
shown when the increments for equal pressure are the same in all 
positions of the diagram. It is important that the piston is not 
cramped or pushed over by the spring, in any part of its stroke. 

Friction of the piston and pencil-movement can be determined 
in the calibration of the indicator-spring as explained. When 
the spring is removed from the indicator, the parts should 
work easily and freely but without lost motion. 

395. Accuracy of the Drum-motion. — The accuracy of the 
drum-motion depends on the form of the drum-spring, the 
mass moved, the length of the diagram, and the elasticity of 
the connecting cord. 

Indicator-drums would revolve in a harmonic motion if 
the inertia of the mass could be neglected. The speed of ro- 
tation is greatest near the half-stroke of the piston ; therefore, 
if the drum-spring tension can be adjusted so as to exactly 
counterbalance the effect of the inertia of the moving parts, 
the theoretical harmonic motion will be nearly realized. 

In most indicator drum-springs the tension increases directly 
in proportion to the extension. Since the speed of the drum 
is greatest at half stroke, at this point the drum will run 
ahead of its theoretic motion if the spring tension is not suffi- 
cient to counteract the effect of the inertia of the moving parts. 
Therefore if the tension of the drum-spring is adjusted to 
exactly balance the effect of inertia at half-stroke, the card 
should be as nearlyas possible theoretically correct. To ob- 
tain the value of this tension, use is made of the formulae for 
the harmonic motion of a body as follows. Let 



540 



EXPERIMEN TA L ENGINEERING. 



[§ 395- 



t = time of \ length of card = \ of a revolution ; 
s = i length of card ; 



t — 



Va 



; (see Church's Mechanics.) 



P — pM — T, where T is the tension in the spring at £ the 
length of the card. 



M 



= — sa\ 
W 



a = — 



== mass of rotating parts ; 



a = 



/. t = 



yws 4 W 



s 

T 
~Ms 



The foot, pound, second system is used in the formulae, 
The results are shown in the following table. 



TABLE FOR TENSION ON INDICATOR DRUM OF i.o lb. 
WEIGHT. 



Revolutions 


Pounds of 


Revolutions 


Pounds of 


per 


Force to pull 


per 


Force to pull 


Minute. 


Drum 1.75 in. 


Minute. 


Drum 1.75 in. 


50 


O IO 


225 


2.5 


75 


O.25 


250 


3.15 


100 


O.50 


275 


3.8 


125 


0.8 


300 


4-55 


150 


I- 15 


350 


6.15 


175 


1-55 


375 


7.0 


200 


2.0 


400 


8.0 



The total error introduced by inertia can be determined as 
follows : Attaching the indicator to an engine, permit it to 
run sufficiently long to harden the cord and the knots, then 
stop the engine, turn it over by hand and find the length of the 
diagram with the speed so small as to eliminate the inertia ; 
leaving the cords connected, run the engine at full speed : any 



§ 395-] THE STEAM-ENGINE INDICATOR. 54 1 

inertia etitct will be shown by an increase in the length of the 
diagram. This increase in length may be partly due to stretch 
in the indicator-cord caused by inertia of the rotating parts, as 
even with the best tension on the springs, determined as ex- 
plained, it may be sensibly lessened by the use of wire. A 
simple arrangement, consisting of a pin and connecting-rod 
leading to the face-plate of a lathe, the tool-rest being utilized 
as a guide, may be used instead of an engine for obtaining 
complete determination of this error. The amount of error 
caused by over-travel of the drum has been found by experi- 
ment to be from 0.5 to 1.5 per cent at 250 revolutions, with the 
best tension on the drum spring. 

Uniform Tension on the Indicator-cord. — It is often impor- 
tant to determine whether the drum-spring maintains a uniform 
tension on the cord, or whether it alternately exerts a greater 




Fig. 253. — Brown Drum-spring Testing-device 



or less stress; this may be determined by the instrument shown 
in Fig. 253. The testing instrument consists of a wooden 
plate, A, on one end of which is fastened the brass frame, BB y 
carrying the slide, C, with its cross-head, D. The head of 
the spring, R, is screwed to the cross-head, while the other 
end is connected with the bent lever, G, carrying the pencil 
The connecting-rod, E, which moves the slide, C, receives 
its motion from a crank not shown in the figure. The 
swinging leaf upholds the paper on which the diagram is to be 
' taken. The indicator to be tested is clamped to the plate as 
shown, and the drum-cord connected with the free end of the 
spring. The crank is made to move at the speed at which 
it is desired to test the drum-spring. The paper is then 
pressed up to the pencil and the diagram taken. If the tension 



542 



EXPERIMENTAL ENGINEERING. 



1% 39^- 



on the cord is constant, the lines which represent the forward 
and return strokes will be parallel to the motion of the slide; 
but, if the stress is not constant, the pencil will rise and fall as 
the stress is greater or less. The line drawn when the cord 
has been detached from the indicator (Fig. 254) is the line of no 
stress. In the diagram, horizontal distance represents the 
position of the drum, and vertical distance represents strain 
on the cord. The perfect diagram would be two lines near 
together and parallel to the line of no stress, and would repre- 
sent a constant stress, and consequently a constant stretch of 
the cord, from which no error would result. 

When the length of the cord and the amount it will stretch 
under varying stresses is known, the errors in the diagram due 
to stretch of cord caused by irregular stresses applied by the 
drum-spring can be calculated. 




Indicator. 250 revolutions 
A 



Indicator. 250 revolutions 




Indicator. 400 revolutions 



Indicator. 400 revolutions 
D 



Fig. 254.— Diagrams showing Variation in Drum-spring Stress. 



396. To Adjust and Calibrate a Drum-spring. 

1. Find the weight of the moving parts, and compute the 
theoretic stress on the indicator-cord. (See Article 395.) 

2. Attach to the face-plate of a lathe in such a manner 
that the speed can be varied within wide limits. 

3. Draw diagrams at various rates of speed, various lengths 
of stroke, and various tensions on the drum-spring. 

4. Find the en or in the diagram for each condition. Plot 
the results, and deduce from the curve shown the best length 
of diagram and best tension for each speed. 



§ 397-] 



THE STEAM-ENGINE INDICATOR. 



543 



5. Repeat the same operations with the Brown spring test- 
ing-device, and compare the results. 

397. Method of Attaching the Indicator to the Cylinder. 
— Holes for the indicator are drilled in the clearance-spaces at 
the ends of the cylinders, in such a position that they are not 
even partially choked by any motion of the piston. These 
holes are fitted for connection to half-inch pipe : they are 
located preferably in horizontal cylinders at the top of the 
cylinder ; but if the clearance-spaces are not sufficiently great 
they may be drilled in the heads of the cylinder, and connec- 
tions to the indicators made by elbows. The holes for the in- 




Fig. 255.— Section of Crosby Three-way Cock. 



Fig. 256. — Elevation of Crosby 
Three-way Cock. 



dicator-cocks are usually put in the cylinders by the makers of 
the engine, but in case they have to be drilled great care must 
be exercised that no drill-chips get into the cylinder. This may 
be entirely prevented by blocking the piston and admitting 
twenty or thirty pounds of steam-pressure to the cylinder. 

The connections for the indicator are to be made as short and 
direct as possible. Usually the indicator-cock can be screwed 
directly into the holes in the cylinder, and an indicator attached 
at each end. In case a single indicator is used to take dia- 
grams from both ends of the cylinder, half-inch piping with as 
easy bends as possible is carried to a three-way cock, as in Fig. 



544 EXPERIMENTAL ENGINEERING. [§ 398. 

194, to which the indicator is attached. The cock is located 
as nearly as possible equidistant from the two ends of the 
cylinder. 

The form of the three-way cock is shown in Figs. 199 and 
200. and the method of connecting in Fig. 194. 

In connecting an indicator-cock, use a wrench very care- 
fully ; but on no account use lead in the connections, as it is 
likely to get in the indicator and prevent the free motion of 
the piston. 

398. Directions for Taking Indicator-diagrams. 

Firstly, provide a perfect reducing-motion, and make ar- 
rangements so that the indicator-drum can be stopped or 
started at full speed of the engine. (See Article 391.) 

Secondly, clean and oil the indicator, and attach it to 
the engine as previously explained. Insert proper spring ; oil 
piston with cylinder-oil. 

Thirdly, put proper tension on the drum-spring (see Article 
395) ; see that the pencil-point is sharp and will draw a fine- 
line. 

Fourthly, connect the indicator-cord to the reducing-motion; 
turn the engine over and adjust the cord so that the indicator- 
drum has the proper movement and does not hit the stops. 

Fifthly, put the paper on the drum ; turn on steam, allow it 
to blow through the relief-hole in the side of the cock ; then 
admit steam to the indicator-cylinder, close the indicator-cock, 
start the drum in motion, and draw the atmospheric line with 
engine and drum in motion ; open the cock, press the pencil 
lightly and take the diagram ; close the cock and draw a second 
atmospheric line. Do not try to obtain a heavy diagram, as all 
pressure on the card increases the indicator friction and causes 
more or less error. Take as light a card as can be seen ; brass 
point and metallic paper are to be used when especially fine 
diagrams are required. 

When the load is varying, and the average horse-power is 
required, it is better to allow the pencil to remain during a 
number of revolutions, and to take the mean effective pressure 
from the several diagrams drawn. 



§ 399-] THE STEAM-ENGINE INDICATOR. 545 

Remove card after diagram has been taken, and on the 
back of card make note of the following particulars, as far as 
conveniently obtainable : 



No Time Date. 

Diagram from M Engine 

Diameter of cylinder 

Length of stroke 

Revolutions per minute , 

Pressure of steam, in lbs., in boiler. 

Position of throttle-valve 

Vacuum per gauge, in inches 

Temperature of hot-well 

Scale of spring , 

Inside diameter of feed-pipe 

" " " exhaust-pipe 

Valves 



Built by. 

Pressure . 

Barometer reads 

..Throttle.. 

Regulator 

Remarks 



Sixthly, after a sufficient number of diagrams has been taken, 
remove the piston, spring, etc., from the indicator while it is 
still upon the cylinder ; allow the steam to blow for a moment 
through the indicator-cylinder, and then turn attention to the 
piston, spring, and all movable parts, which must be thoroughly 
wiped, oiled, and cleaned. Particular attention should be paid 
to the springs, as their accuracy will be impaired if they are al- 
lowed to rust ; and great care should be exercised that no gritty 
substance be introduced to cut the cylinder or scratch the 
piston. Be careful never to bend the steel bars or rods. 

399. Care of the Indicator. — The steam-engine indicator 
is a delicate instrument, and its accuracy is liable to be im- 
paired by rough usage. It must be handled with care, kept 
clean and bright ; its journals must be kept oiled with suitable 
oil. It must be kept in adjustment. In general, all screws can 
be turned by hand sufficiently tight,' and no wrench should be 
used to connect or disconnect it. Never use lead on the con- 
nections. Before using it, take it apart, clean and oil it. Try 
each part separately. See if it works smoothly ; if so, put it 
together without the spring. Lift the pencil-lever, and let it 



546 EXPERIMENTAL ENGINEERING. [§399- 

fall ; if perfectly free, insert the spring as explained, and see that 
there is no lost motion ; oil the piston with cylinder-oil, and all 
the bearings with nut- or best sperm-oil. Give it steam, but do 
not attempt to take a card until it blows dry steam through the 
relief. If the oil from the engine gums the indicator, always 
take it off and clean it. After using it remove the spring, dry 
it and all parts of the indicator, then wipe off with oily waste. 
Fasten the indicator in its box, in which it will go, as a rule, 
only one way, but it requires no pounding to get it properly in 
place ; carefully close the box to protect it from dust. 



CHAPTER XVII. 



THE INDICATOR-DIAGRAM. 



400. Definitions. — The indicator-diagram is the diagram 
taken by the indicator, as explained in Article 378, page 515. 

In the diagram the ordinates correspond to the pressures 
per square inch acting on the piston, the abscissae to the travel 




Fig. 257.— Diagram from an Improved Greene Engine. Cylinder, 16 Inches in Diameter, 
36 Inches Stroke. Boiler-pressure, ioo lbs. 80 Revolutions per minute. Scale, 50. 

of the piston. During a complete revolution of an engine 
occur four phases of valve- motion which are shown on the indi- 
cator-diagram, viz. : admission, CDE, when the valve is open 
and the steam is passing into the cylinder ; expansion, EF t 
when steam is neither admitted nor released and acts by its 

547 



54 8 EXPERIMENTAL ENGINEERING. [§ 40a 

expansive force to move the piston ; exhaust, FGH, when 
the admission-port is closed and the exhaust opened so that 
steam is escaping from the cylinder; and compression, HC y 
when all the ports are closed and the steam remaining in the 
cylinder acts to bring the piston to rest. 

The Atmospheric Line, AB, is a line drawn by the pencil of 
the indicator when the connections with the engine are closed 
and both sides of the piston are open to the atmosphere. This 
line represents on the diagram the pressure of the atmosphere,, 
or zero gauge-pressure. 

The Vacuum Line, OK, is a reference-line drawn a distance 
corresponding to the barometer-pressure (usually about 14.7 
pounds) by scale below the atmospheric line. It represents a 
perfect vacuum, or absence of all pressure. 

The Clearance Line, OY, is a reference-line drawn at a dis- 
tance from the end of the diagram equal to the same per cent 
of its length as the clearance or volume not swept through by 
the piston is of the piston-displacement. The distance between 
the clearance line and the end of the diagram represents the 
volume of the clearance of the ports and passages at the end of 
the cylinder. 

The Line of Boiler -pressure, JK, is drawn parallel to the 
atmospheric line, and at a distance from it by scale equal to 
the boiler-pressure shown by the gauge. The difference in 
pounds between it and DE shows the loss of pressure due to 
the steam-pipe and the ports and passages in the engine. 

The Admission Line, CD, shows the rise of pressure due to 
the admission of steam to the cylinder by opening the steam- 
valve. If the steam is admitted quickly when the engine is 
about on the dead-centre, this line will be nearly vertical. 

The Point of Admission, C, indicates the pressure when the 
admission of steam begins at the opening of the valve. 

The Steam Line, DE, is drawn when the steam- valve is open 
and steam is being admitted to the cylinder. 

The Point of Cut-off, E, is the point where the admission 
of steam is stopped by the closing of the valve. It is difficult 
to determine the exact point at which the cut-off takes place* 



:§ 4°°-J THE INDICATOR DIAGRAM. 549 

It is usually located where the outline of the diagram changes 
its curvature from convex to concave. It is most accurately 
determined by extending the expansion line and steam line so 
that they meet at a point. 

The Expansion Curve, EF, shows the fall in pressure as the 
steam in the cylinder expands doing work. 

The Point of Release, F, shows when the exhaust-valve 
opens. 

The Exhaust Line, FG, represents the change in pressure 
that takes place when the exhaust-valve opens. 

The Back pressure Line, GH, shows the pressure against 
which the piston acts during its return stroke. On diagrams 
taken from non-condensing engines it is either coincident with 
or above the atmospheric line, as in Fig. 201. On cards taken 
from condensing engines it is found below the atmospheric 
line, and at a distance greater or less according to the vacuum 
obtained in the cylinder. 

The Point of Exhaust Closure, H, is the point where the 
exhaust-valve closes. It canno^ be located very definitely, as 
the first slight change in pressure is due to the gradual closing 
of the valve. 

The Point of Compression, H, is where the exhaust-valve 
closes and the compression begins. 

The Compression Curve, HC, shows the rise in pressure due 
to the compression of the steam remaining in the cylinder 
after the exhaust-valve has closed. 

The Lnitial Pressure is the pressure acting on the piston 
at the beginning of the stroke. 

The Terminal Pressure is the pressure above the line of 
perfect vacuum that would exist at the end of the stroke if 
the steam had not been already released. It is found by con- 
tinuing the expansion curve to the end of the diagram, as in 
Fig. 201. This pressure is always measured from the line of 
perfect vacuum, hence it is the absolute terminal pressure. 

Admission Pressure is the pressure acting on the piston at 
end of compression, and is usually less than initial pressure. 



550 EXPERIMENTAL ENGINEERING. [§ 4OCX 

Compression Pressure is the pressure acting on the piston at 
beginning of compression ; this is also the least back pressure. 

Cut-off Pressure is the pressure acting on the piston at 
beginning of expansion. 

Release Pressure is the pressure acting on the piston at end 
of expansion. 

Mean Forward Pressure is the average height of that part 
of the diagram traced on the forward stroke. 

Mean Back Pressure is the average height of that part 
traced on the return stroke. 

Mean Effective Pressure (M. E. P.) is the difference between 
mean forward and mean back pressure during a forward and 
return stroke. It is the length of the mean ordinate inter- 
cepted between the top and bottom lines of the diagram mul- 
tiplied by the scale of the diagram. It is obtained without 
regard to atmospheric or vacuum lines. 

Ratio of Expansion is the ratio of the volume of steam in 
the cylinder at end of the stroke, compared with that at cut- 
off. In computations for this quantity the volume of clear- 
ance must be taken into account. Ratio of expansion is 
denoted by r. For hyperbolic expansion,/ being pressure in 
pounds per square foot at cut-off, and v the corresponding 
total volume, the work done per stroke and per square foot of 
area = pv{\ -f- Hy log r). 

The volume may be expressed as proportional to linear 
feet, with an additional length equal to the per cent of clear- 
ance, since the area of the cylinder is constant. The product 
of pressure per square foot into total volume is a constant 
quantity for hyperbolic expansion. The ratio of expansion is 
the reciprocal of the cut-off measured from the clearance line. 
This cut-off is distinguished from that shown directly on the 
card by designating it as the absolute cut-off. 

Initial Expansion is the fall of pressure during admission, 
due to an imperfect supply of steam. 

Wire -drawing is the fall of pressure between the boiler 
and cylinder; it is usually indicated by initial expansion. 



§ 4 oi.j 



THE INDICA TOR-DIA GRAM. 



551 



401. Measurement of Diagrams. — The diagrams taken 
are on a small scale, they are often irregular, and the boundary 
lines are frequently obscure, so that the measurement must be 
made with great care. 

The diagrams may be taken from each end of the cylinder 
on a separate card, as shown in Fig. 257; or by the use of the 
three-way cock (see Article 398), in which case the two dia- 
grams will be drawn on the same card as shown in Fig. 258. In 
the latter case each diagram is to be considered separately; that 
is, the area of each diagram, as CDEBFC and GHIJKG, is to 




Fig. 258. 



be determined as though on a separate card. The object of 
diagram-measurements is principally to obtain the mean effect- 
ive pressure (M. E. P.). 

Two methods are practised. 

First, the method of ordinates. In this case the atmos- 
pheric line AB is divided into ten equal spaces, and ordinates 
are erected from the centre of each space. The sum of the 
length of these various ordinates divided by the number gives 
the mean ordinate. This multiplied by the scale of the dia- 
gram gives the mean effective pressure. The sum of the 
ordinates is expeditiously obtained by successively transferring 
the length of each ordinate to a strip of paper and measuring 
its length. 

Secondly, with the planimeter. The planimeter gives the 
mean ordinate much more accurately and quickly than the 



552 



EXPERIMENTAL ENGINEERING. 



[§ 4°2, 



method of ordinates. The various planimeters are fully 
described, pages 32 to 55. 

With any planimeter the area of the diagram can be ob- 
tained, in which case the mean ordinate is to be found by 
dividing by the length of the diagram. Several of the pla- 
nimeters give the value of the mean ordinate, or M. E. P., 
directly. 

In some instances the indicator-diagram has a loop, as in 
Fig. 2 59, caused by expanding below the back-pressure line; in 
this case the ordinates to the loop are negative and should be 




Fig. 259. 



subtracted from the lengths of the ordinates above. In case 
of measurement by the planimeter, if the tracing-point be 
made to follow the expansion-line in the order it was drawn by 
the indicator-pencil, the part within the loop will be circum- 
scribed by a reverse motion, and will be deducted automatically 
by the instrument, so that the reading of the planimeter will 
be the result sought. 

402. Indicated Horse-power. — Indicated horse-power is 
the horse-power computed from the indicator-diagram, being 
obtained by the product of M. E. P. (/), length of stroke in 
feet (/), area*of piston in square inches (a), and number of revolu- 
tions (n), as represented in the formula plan ~ 33,000. In this 
computation the area on the crank side of the piston is to be 
corrected for area of piston-rod, and the two ends of the cylin- 
ders computed as separate engines. Further, in this computa- 
tion, it will not in general answer to multiply the average 
M.E.P. of a number of cards by the length of stroke and by the 



§403-] . THE INDICATOR-DIAGRAM. 553 

average of the number of revolutions, but each card must be 
subjected to a separate computation and the results averaged. 
This can be readily done for each engine by computing a table 
made up of the products of the average value of n by length 
of stroke and area of piston, and for different values of M. E. P. 
from 1 to 10. Take from this table the values corresponding to 
the given M. E. P., increase or diminish this as required by 
the per cent of change of speed from the average. A very 
convenient table for this purpose, entitled " Horse-power per 
Pound, Mean Pressure," is given in the Appendix to this work, 
arranged with reference to diameter of cylinder in inches and 
piston-speed in feet per minute. 

403. Form of the Indicator-diagram. — The form of the 
indicator-diagram has been carefully worked out for the ideal 
case by Rankine and Cotterell.* In the ideal case the steam 
works in a non-conducting cylinder, and all loss of heat is due 
to transformation into work, the expansion in such a case being 
adiabatic. In the actual case the problem is much more com- 
plicated, since a large portion of the heat is utilized in heating 
the cylinder, and is returned to the steam at or near the time 
of exhaust; doing little work. It is found, however, in the best 
engines working with quick-acting valve-gear, that the steam 
and back-pressure lines are straight and parallel to the atmos- 
pheric line, and that the expansion and compression lines are 
very nearly hyperbolae, asymptotic to the clearance line and 
to the vacuum line. 

If we denote by p the pressure measured from the vacuum 
line, and by v the volume corresponding to a distance meas- 
ured from the clearance line, so that pv shall be the co-ordinates 
of any point, we shall have as characteristic of the hyperbola 

pv = constant. 

This is the same as Mariotte's law for the expansion of non- 
condensible gases, since, according to that law, the pressure 
varies inversely as the volume. 

* Steam-engine, by James H. Cotterell. 



5 54 



EXPERIMENTAL ENGINEERING. 



[§404. 



Rankine found by examination of a great many actual cases 
that the expression pv* = constant agrees very nearly with the 
ideal case of adiabatic expansion. The variation from the ideal 
expansion line in any given case may be considerable, and the 
hyperbola drawn from the same origin is considered as good a 
reference-line as any that can be used, and the student should 
become familiar with the best methods of constructing it. 

404. Methods of Drawing an Hyperbola. — The methods 
of drawing an hyperbola, the clearance and vacuum lines being 
given, are as follows : 

First Method. (See Fig. 260.) — CB, the clearance line, and 
CD, the vacuum line, being given, draw a line parallel to the 




Fig. 260. — Method of Drawing an Hyperbola. 



atmospheric line through B ; find by producing the steam and 
expansion lines the point of cut-off, c. Draw a series of 
radiating lines from the point C to the points E, F, G, H, and 
A, taken at random, and a line cb intersecting these lines, 
drawn from c parallel to BC. From the points of the inter- 
section of cb with these radiating lines draw horizontal lines to 
meet vertical lines drawn from the points E, F, G, H, and 



§ 405-] 



THE INDICATOR-DIAGRAM. 



555 



A ; the intersections of these lines at e, f, g, /i, and a are points 
in the hyperbola passing through the point c. If it is desired 
to produce the hyperbola from a upward, the same method is 
used, but the line AB is drawn through the point <z, and the 
vertical lines are extended above A B instead of below. 

Second Method. (See Fig. 261.) — The hyperbola may be 
drawn by a method founded on the principle that the inter- 
cepts made by a straight line intersecting an hyperbola and its 
asymptotes are equal. Thus if abed represent an hyperbola, 
BC and CD its asymptotes, then the intercepts act' and bb' 
made by the straight line a' b' are equal. 

To draw the hyperbola : Beginning at any point, as a, draw 




b ' d 

Fig. 261.— Method of Drawing an Hypkrbola. 



the straight line a'b\ and lay off from the line CD b'b, equal to 
a' a ; then will b be one point in the hyperbola. Draw a similar 
line c'd r through b, making d'e equal c'b ; then will c be another 
point in the hyperbola. This process can be repeated until a 
suitable number of points is found ; the hyperbola is to be 
drawn through these points. A similar method can be used 
to draw the hyperbola EF. 

405. Construction of Saturation and Adiabatic Curves. 
— The saturation curve of steam is represented almost exactly 
by the equation pv& = a constant. This is the curve whose 



556 EXPERIMEN TA L ENGINEERING. [§ 40 5 . 

volumes and pressures correspond to those given in the steam- 
tables ; no doubt the easiest way to construct such a curve is 
to take the volumes from the steam-tables corresponding to 
given pressures and set them off along the volume axis ; lay 
off the corresponding pressures as ordinates ; then a curve 
drawn through the extremities of the ordinates will be the ex- 
pansion curve, which, as the form of the equation shows, does 
not differ greatly from an hyperbola. 

The adiabatic curve, or that corresponding to neither gain 
nor loss of heat, is expressed approximately bypirs° = constant,* 
and differs somewhat more from the hyperbola than the satu- 
ration curve. 

Any of the exponential curves which are represented by 
the equation /?/* =p 1 v 1 n = p^v" can be drawn as follows : 

From the above expression 

n log v -\- log/ = 71 log v x -f- log/j , 

from which 

log/ = n log v x -f- log/ x — n log v ; 

from which, if ;/, v x , and v are known,/ may be determined. 
The values of n are as follows : 

Equilateral hyperbola, n = I ; 
Saturation curve — steam, n = ±% = 1.0646; 
Adiabatic curve — steam, n = 1.035 +0- I 4*> 

" gas, 71 = 1.408; 
Isothermal " " n = 1.0. 

These three expansion curvesf are represented in Fig. 262 ; 
the pressures from o to 90 pounds per square inch are repre- 
sented by the ordinates, and the volumes in cubic feet corre- 
sponding to one pound in weight are represented by abscissae. 

* Rankine's Steam-engine, page 385. 

f See Thurston's Engine and Boiler Trials, page 251. 



§ 4o6.] 



THE INDICATOR-DIAGRAM. 



557 



In the figure the curve A to G is the hyperbola, A to / the 
saturation curve, and A to L the adiabatic curve. ON is the 
axis of the hyperbola, of which OB and OH are asymptotes. 
It is to be noticed that the saturation curve corresponds to a 
uniform quality of steam, the adiabatic curve to a condition 
in which the moisture is increasing, and the hyperbolic curve 




1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 
Fig. 262.— The Three Expansion Curves. 



300 300 



to a condition in which the moisture is decreasing, the latter 
agreeing more closely with the actual condition. 

406. Weight of Steam from the Indicator-diagram. — 
The diagram shows by direct measurement the pressure and 
volume at any point in the stroke of the piston ; the weight 
per cubic foot for any given pressure may be taken directly 
from a steam-table. The method, then, of finding the weight 
of steam for any point in the stroke is to find the volume in 
cubic feet, including the clearance and piston displacement to 
the given point, which must be taken at cut-off or later, and 
multiply this by the weight per cubic foot corresponding to 
the pressure at the given point as measured on the diagram. 
This will give the weight of steam in the cylinder accounted 
for by the indicator-diagram, per stroke. In an engine work- 
ing with compression, the weight of steam at terminal pressure 



558 EXPERIMENTAL ENGINEERING. [§ 4°6- 

filling the clearance-space is not exhausted ; this weight, com- 
puted for a volume equal to clearance -and with weight per 
cubic foot corresponding to compression pressure, should be 
subtracted from the above. This may be reduced to pounds 
of steam per I. H. P. per hour, by multiplying by the number 
of strokes required to develop one horse-power per hour of 
time. 

The method of computing would then be : Find the weight 
per cubic foot, from a steam-table corresponding to the abso- 
lute pressure, at the given point, multiply this by the corre- 
sponding volume in cubic feet, including clearance, and this by 
the number of strokes per hour. Correct this for the steam 
imprisoned in the clearance-space. Divide this by the horse- 
power developed, and we shall have the consumption in pounds 
of dry steam per I. H. P. as shown by the diagram. Thus let. 

A '— area of piston in square feet ; 

a= " " " " " inches; 
N —~ number of strokes per hour; 

n= " " " " minute; 

w = weight of cubic foot of steam at the given pressure ; 

/ = total length of stroke in feet ; 

4 = length of stroke in feet- to point under consideration ; 

c = per cent of clearance; I' = 4 + cl\ b = corresponding 
per cent ; 
w' = weight of cubic foot of steam at compression pressure. 

Then the consumption of dry steam in pounds per hour per 
horse-power (indicated). 

„ NAl„ , N 6ol na(bw — cw') is,7$o[l>iv—cw''] 

33>ooo 

The above equation corrects for the steam caught in the 
clearance spaces during compression. 

As an example: Compute the steam consumption as shown 
in Fig. 257 at point of cut-off E and at terminal pressure. 



§406.] THE INDICATOR-DTAGRAM. 559 

The absolute pressure shown by the diagram is 97 pounds 
at cut-off and 37 at end of the stroke. Neglect steam in clear- 
ance. 

The length of stroke total is 3 feet, at cut-off is J foot. 

Clearance is 3.2 per cent. M. E. P. (p) is 50 pounds. 

Steam-consumption at Cut-off. — From steam-table w=o.22o8. 

5= 13.750 (02 5 2 08)(a75 +°^^i6.. 7 lb S . per LH.P.per hour. 

St earn- consumption at End of Stroke. — From steam-table 
w = 0.0896. 

S=I 3 i7S0 ^^(3±o^9) = 2537lbsperIHpperhour 



This, it should be noticed, is not the actual weight of steam 
used per horse-power by the engine, but is that part which cor- 
responds to the amount of dry steam remaining in the cylinder 
at the points under consideration. The amount is usually less 
when computed at cut-off than at the end of the stroke, since 
some of the steam which was condensed when the steam first 
entered the cylinder is restored by evaporation during the latter 
portion of the period of expansion. 

The equations and examples as given above apply only to 
a simple engine. They may be applied to a compound or triple- 
expansion engine by considering that all the work is done in the 
low-pressure cylinder as represented on a combined diagram. 
In such a case, p of the formula would equal the equivalent 
M. E. P. for the combined diagram. That is, p'/r + p"=p, 
in which r is the ratio of the areas of the cylinders, p' the M. E. P. 
of the high-, and p" that of the low-pressure cylinder. 

If we consider the steam- consumption only for the end of 
the stroke, l a of equation (1) becomes equal to /, and the equation 
reduces to the following form : 

w 
St = i3>75°j( 1 +c) (2) 



560 EXPERIMENTAL ENGINEERING. [§ 407. 

Neglecting the clearance, 

4=13,750-; ........ (3) 

in which / = the M. E. P. of the diagram, and w the weight 
per cubic foot corresponding to the terminal pressure. For- 
mula (3) has been tabulated as follows : 

Thompson's tables, given in the Appendix, give values of 
13,7502^, and the tabular values must be divided by the M. E. P. 
to give the steam-consumption per I. H. P. per hour. 

Tabor's tables give values of , and the tabular values 

P 
must be multiplied by the weight of a pound of steam corre- 
sponding to the terminal pressure, to give the steam-consump- 
tion. 

Williams's tables, published in the Crosby catalogue, give 

values of — — — , and the results in each case have to be multi- 

42543 
plied by 32. ^2w to give the steam-consumption. 

A graphical correction is made in all cases for compression 
by drawing a horizontal line through the terminal pressure to 
compression line of diagram, and multiplying the result given 
in the table by the ratio of the portion of this line intercepted 
between terminal point and compression, to the whole stroke. 

407. Clearance Determined by the Diagram. — The 
clearance is usually to be determined by actual measurement 
of the volume of the spaces not swept through by the piston, 
and comparing this result with the volume of piston-displace- 
ment, the ratio being the clearance. Since the expansion and 
compression lines of the diagram are nearly hyperbolae, the 
clearance line can be drawn by a method nearly the reverse of 
that used in constructing an hyperbola (Article 404). 

In this case proceed as follows: Lay off the vacuum line 
CD (Fig. 207) parallel to the atmospheric line FT, and at 
a distance corresponding to the atmospheric pressure. The 
position of the clearance line can be determined by two methods, 
corresponding to those used in drawing the hyperbola. First 



§ 4o8.] 



THE INDICATOR-DIAGRAM. 



5 6l 



method: Take two points, a and b in the expansion curve and 
c and d in the compression line, and draw horizontal and 
vertical lines through these points, forming rectangles aa'bb' 
and cc'dd- '. Draw the diagonal of either rectangle, as a'b' , to 
meet the vacuum line CD: the point of intersection C will be 




_^L \ ? V^-o 

Fig 263. — Methods of Finding the Clearance. 

a point in the clearance line CB, and the clearance will equal 
CN -T- FT. Second method: Draw a straight line through 
either curve, as mn through the compression curve or ef 
through the expansion curve, and extend it in both direc- 
tions. On the line m'n' lay off tin! equal to mm\ or on the 
line e'f lay off ee' equal to ff ; then will either of the points 
e' or n' be in the clearance line and the line drawn perpendicular 
to the vacuum line through either of these points is the clear- 
ance line. In an engine working with much compression the 
clearance will be given more accurately from the compression 
curve than from the expansion curve, since it is more nearly 
an hyperbola. 

408. Re-evaporation and Cylinder Condensation. — By 
considering the hyperbolic curve as a standard, an idea can be 
obtained of the restoration by re-evaporation and the loss by 



562 



EXPERIMENTAL ENGINEERING. 



is 409. 






cylinder condensation. Thus in Fig. 264, suppose that a is 
the point of cut-off at boiler-pressure, construct an hyperbola 
as explained ; in the example considered it is seen to lie above 
the expansion line for a short distance after cut-off, then to cross 
the line at b, and remain below it nearly to the end of the 
stroke. The amount by which the expansion line rises above 
the hyperbola may be considered as due to re-evaporation. 
The area of the diagram lying above would represent the work 
added by heat returned to the steam from the cylinder. 

The methods for determining the cylinder condensation are 




* b' d' 

Fig. 264. — Work Restored by Re-evaporation. 

similar to this process, except that the hyperbola is usually 
drawn upward from the point corresponding to the terminal 
pressure, to meet a horizontal line drawn to represent the boiler- 
pressure, as follows : 

This construction is shown by the dotted lines in the 
diagrams in Fig. 265. The area of the figure enclosed by the 
dotted lines, compared with that of the diagram, is the ratio 
that the ideal diagram bears to the real ; the difference is the 
loss by cylinder condensation. 

The student should understand that both these methods 
are approximations which may vary much from the truth. 

409. Discussion of Diagrams. — Diagrams are often taken 



§409-] 



THE INDICATOR-DIAGRAM. 



5 6 3 



where some portion of the engine is out of adjustment, or the 
indicator or reducing motion is not in perfect order. It is often 



i. Steam 80 lbs. 



91 per cent of ideal. 
40.0 Horse Power 






60 lbs.Boiler Press. 




90 per cent of ideal. 


/y 


r- 






62.4 Horse Power 


^ 








1 



























53 per cent of Ideal. 




65 lbs.Boiler Press. 

r\ 


54 per cent of ideal. 
. 15 Horse Power 







Fio 265.— Loss by Cylinder-condensation. 

possible in such cases to determine the defect from the dia- 
gram, and to suggest the proper remedy. A few examples are 
submitted. Such examples could be multiplied indefinitely, 
and skill and experience will, in general, be required to prop- 
Bottom - of cylinder 

Steam "side. 




Vacuum side- 
Fig. 266. — Unsymmetrical Valve-setting. 



eriy interpret them. Thus Fig. 266 is an illustration of a dia- 
gram taken when the valves were set unsymmetrically. Curves 
or waves in the expansion or compression lines indicate inertia- 



564 



EXPERIMEN TA L ENGINEERING. 



[§409. 



effects in the drum-motion, which is sometimes sufficient to 
make the compression line concave when it should be convex, 
as shown in the lower diagram of Fig. 267. Vertical curves 
are due in large measure to vibrations in the pencil-lever and 
indicator-spring ; they are usually excessive with a light spring 
and high speed. In the case of an automatic engine running 
under variable loads, each revolution will show a different dia- 
gram, as shown in Fig. 267. 



^a 




Fig. 267. — Variation i.f Load. 

Different Forms of Admission-lines. — The form of the ad- 
mission-line is changed* according to the relative time of valve- 
opening and position of piston in its stroke. 

The normal form is shown at A. In B C D and E the valve 
opens late, and after the piston has started on its return stroke t 
In F and G the exhaust-valve closes late, so that live steam 
escapes. H and / are familiar examples of extreme compres- 
sion, produced on high-speed automatic engines working with 
a light load. J shows a sharp corner above the compression 



* Power, September 1891. 



§ 4io.] 



THE IND1 CA TOR-DIA GRA M. 



565 



line, and in general indicates too much lead. In case the valve 
opens too early, the admission-line leans as at K. 

410. Diagrams from Compound and Triple-expansion 
Engines. — The diagram from any cylinder of a compound or 
triple-expansion engine is not likely to differ in any noticeable 






Fig. 268.— Typical Admission-lines. 



particular from those taken from a simple engine as already 
described. They are usually taken with different springs for 
the different cylinders, but may have very nearly or exactly 
the same lengths. 

The diagrams from a compound engine may be reduced to 
an equivalent diagram, taken from a single cylinder by the fol- 
lowing method : Lay off a vertical line OB, and a horizontal 
line PQ. Let PQ be the vacuum line, and BC the line of 



566 



EXPERIMENTAL ENGINEERING. 



[§4IO. 



highest steam-pressure acting in the small cylinder. Lay off 
ON proportional to the volume of the small cylinder, and OP 
proportional to the volume of the large cylinder. Let FA be 
the line of back pressure of the large cylinder, AD that of 
the small cylinder : then BCD A is the diagram from the small 
cylinder, EKFA that from the large cylinder. 

To combine them into one diagram, draw a line KGJf par- 
allel to POQ, intersecting both diagrams, and lay off upon it 
HL = KG ; and GL — GH-\- KG represents the total volume 





K^ 


E 


B C 








G H/ 


D 






< — ' 






^^ 




M 


F 




A 




f 


D 




( 


d r 


\ Q 



Fig. 269. 

in both cylinders when the pressure is OG, and L is a point in 
the expansion line the same as though the action took place 
in the large cylinder only. In the same way other points may 
be found, and the line CDLM drawn. This diagram may be 
discussed as if it represented the steam acting in the large 
cylinder only. 

Fig. 270 is a combined diagram from a triple-expansion 
engine,* in which the cylinders have the ratio of I : 2.25 : 2.42, 
and the total ratio of expansion is 8. The length of each dia- 
gram is made proportional to the total volume of the cylinder 
from which it was taken ; the diagrams are all drawn to the 
same scale of pressures, and each is located at a distance from 
a vertical line proportional to the volume of its clearance. 
From the point of cut-off corresponding to boiler-pressure an 
hyperbola is drawn as has been explained, and the area sur- 
rounding the diagrams is shaded. The work done in the three 
cylinders can be computed from the diagram as though done 
in one only. 



* See Thurston's Engine and Boiler Trials, page 202. 



55 4"-] 



THE INDICATOR-DIAGRAM. 



567 



411. Crank-shaft and Steam-chest Diagrams.— Dia- 
grams may be taken with the motion of the indicator-drum 
proportional to any moving part of the engine, as for instance 
the crank-shaft. 




Fig. 270. — Combined Diagram from Triple-expansion Engine. 

In such a case, shown by Fig. 271 the ordinates will be as 
before proportional to the pressures per square inch acting on 
the piston, but the abscissae will correspond to distances moved 




Fig. 271,— Shaft-diagram. 

through by the crank-pin. In Fig. 271, A to B is the exhaust, 
from B to C compression, D to E steam line, E to A expan- 
sion. Diagrams may also be taken with the indicator mounted 
on the valve-chest ; in this case the indicator would show vari- 
ation in pressure in the steam-chest. 



568 



EXPERIMENTAL ENGINEERING. 



[§4U 




CHAPTER XVIII. 
METHODS OF TESTING THE STEAM-ENGINE. 

412. Standards Employed in Engine-testing. — The 

unit of work ordinarily used in engine-testing is the horse-power 
(H.P.), which may be either that shown by the indicator and 
known as the indicated horse-power (I.H.P.), or that delivered 
from the engine, which is known as delivered or brake horse- 
power (D.H.P.). The horse-power is equivalent to 33,000 
foot-pounds or 42.413 B.T.U. per minute, or to 1,980,000 foot- 
pounds or 2545 B.T.U. per hour. 

Fuel, Steam,, and Heat Consumption. — The ordinary standard 
of comparison of the economy of the work done by different 
engines is the weight of fuel or steam, or the number of B.T.U- 
required by the engine for each horse-power of work indicated 
or delivered per hour. The heat consumption, B.T.U. per 
H.P. hour, presents the advantages over the others of being 
more concise and definite. 

Duty. — This term is applied to the work performed by pump- 
ing-engines, expressed in foot-pounds, for the consumption of 
100 pounds of coal, 1000 pounds of steam, or 1,000,000 B.T.U. 
See Art. 254. 

Perfect Engine. — The performance of a perfect engine is 
frequently employed as a standard of comparison. The per- 
fect engine is one which transforms all the available heat received 
and not rejected into mechanical work. Such an engine operates 
in a reversible or Carnot cycle and has a thermodynamic efficiency 
of (Ti — T 2 )/Ti, in which T\ is the absolute temperature of the 
entering steam and T 2 that of the exhaust. 

The heat (B.T.U.) consumed per H.P. hour for an engine 
of this kind is evidently 

h = 2545 T 1 /(T 1 ~T 2 ). 

The least possible weight of steam will be used in the per- 

5 6 9 



'■&& 



570 EXPERIMENTAL ENGINEERING. [§ 413 

feet engine when the difference between the heat entering, A, 
and that discharged, q, has all been converted into work. Hence 
the least possible steam consumption per H.P. hour of the per- 
fect reversible engine is 

2545 
*-q \Ti 

Rankine Cycle. — The maximum amount of heat which can 
be transformed into work in the perfect non-reversible engine 
is given by Professor Rankine per pound of steam as follows: 

K = T 1 -T 2 -T 2 \o^ + r(i-^j. 

This expression is frequently used as a standard of com- 
parison by British engineers, and the cycle on which such an 
engine works is termed the Rankine cycle. 

The efficiency of the steam-engine is expressed in various 
ways as follows: 

1. Thermal Efficiency. — This is the ratio of the work actu- 
ally done (A.W.), expressed in heat units, to the total heat sup- 
plied (Q) in the steam. It is equal to AW/Q. 

2. Thermodynamic Efficiency. — This is the greatest possible 
ratio of work done by the working substance to the mechanical 
equivalent of the heat expanded on it to do that work. In the 
Carnot reversible cycle this efficiency equals (T 1 — T 2 )/T 1 . 

3. Mechanical Efficiency. — This is the ratio of the work 
actually delivered (D.H.P.) to that done on the piston and shown 
by the indicator (I.H.P.). 

4. Plant Efficiency. — This is equal to the product of the 
several efficiencies of the various parts or machines which com- 
pose the plant. 

413. Objects of the Engine-test. — The test may be 
made: 1. To adjust the valves or working parts of the engine. 

2. To determine the indicated or dynamometric horse-power. 

3. To ascertain the friction for different speeds or conditions. 

4. To determine the consumption of fuel or steam per horse- 
power per hour. 5. To investigate the heat-changes which 



; 



§ 4 1 4-] METHODS OF TESTING THE STEAM-ENGINE, 5/1 

characterize the passage of the steam through the engine. 
The general method of the test will depend largely on the ob- 
ject for which the test is made ; in any event the apparatus to 
be used should be carefully calibrated, the dimensions of the 
engine obtained, and the test conducted with care. 

414. Measurements of Speed. — The various instruments 
employed for measurement of speed are speed-indicators, ta- 
chometers, continuous counters, and chronographs. 

Where the number of revolutions only is required, it is 
usually obtained either by counting or by the hand speed- 
indicator. Counting can be done quite accurately without an 




Fig. 273. — Double-ended Speed-indicator. 



instrument, by holding a stick in the hand in such a position 
that it is struck by some moving part, as the cross-head of an 
engine, once in each revolution. The hand speed-indicator, of 
which one form is shown in Fig. 273, consists of a counter 
operated by holding the pointed end of the instrument in the 
end of the rotating shaft. In using the instrument, the time 
is noted by a watch at the instant the counting gears are put 
in operation or are stopped. A stop-watch is very convenient 
for obtaining the time. The errors to be corrected are princi- 
pally those due to slipping of the point on the shaft, and to the 
slip of the gears in the counting device in putting in and out 
of operation. The best counters have a stop device to prevent 
this latter error, and the gears are engaged or disengaged with 



572 



EXPERIMENTAL ENGINEERING. 



[§ 4H. 



the point in contact with the shaft. To prevent slipping of 
the point, the end of the instrument is sometimes threaded 
and screwed into a hole in the end of the shaft. 

The continuous counter consists of a series of gears arranged 
to work a set of dials which show the number of revolutions. 
The arrangement of gearing in such an instrument is shown in 
Fig. 274. The instrument can usually be made to register by 
either rotary or reciprocating motion, and can be had in a 




Fig. 274. 



square or round case. The reading of the counter is taken at 
stated intervals and the rate of rotation calculated. 

Tachometers (see Fig. 275) are instruments which utilize the 
centrifugal force in throwing outward either heavy balls or a 
liquid. The motion so caused moves a needle a distance pro- 
portional to the speed, so that the number of revolutions is 
read directly from the position of the needle on the graduated 
dial. The tachometer is arranged with a pointed end to hold 
against the shaft whose speed is to be determined, or with a 
pulley so that it may be driven by a belt. 



§4 I 5-] METHODS OF TESTING THE STEAM-ENGINE. 573 

Brown s Speed-indicator consists of a U-shaped tube joined 
to a straight tube in the centre. The revolution of the U-tube 
around the centre tube induces a centrifugal force which ele- 




FlG. 275.— ICHAEFFER AND BUDEXBERG HAND TACHOMETER. 

vat£s mercury in the revolving arms and depresses it in the 
centre tube. A calibrated scale gives the number of revolu- 
tions corresponding to a given depression. 

415. The Chronograph. — The chronograph,* Fig. 276, con- 
sists of a drum revolved by clock-work so as to make a 




Fig. 276. 



definite number of revolutions per minute. A carriage hav- 
ing one or two pens, h, g, as may be required is moved parallel 

* See Thurston's Engine and Boiler Trials, page 226. 



574 EXPERIMENTAL ENGINEERING. [§4*5. 

to the axis of the cylinder by a screw which is connected with 
the chronograph-drum A by gearing. 

The pen in its normal condition is in contact with the paper, 
and it is so connected to an electro-magnet that it is moved 
axially on the paper whenever the circuit is broken. The cir- 
cuit may be broken automatically by the motion of a clock, or 
by hand with a special key, or by any moving mechanism. 
1 wo pens are usually employed, one of which registers auto- 
matically the beats of a standard clock ; the other may be ar- 
ranged to note each revolution or fraction of a revolution of a 
revolving shaft. The distance between the marks made by 
the clock gives the distance corresponding to one second of 
time ; the distance between the marks made by breaking the 
circuit at other intervals represents the required time which is 
to be measured on the same scale. 

This instrument has been in use by astronomers for a long 
time for minute measurements of time, and by its use intervals 
as short as one one-hundredth (.01) part of a second can be 
measured accurately. 

Tuning-fork Chronograph. — A tuning-fork emitting a musi- 
cal note makes a constant and known number of vibrations. 
The number of vibrations of the fork corresponding to the 
musical tones are as follows : 

Note C D E F G A B C a 

Vibrations ) _ zr i /r 

128 144 160 170I 192 213^ 240 256 



per second. 

If now a small point or stylus be attached to one of the 
arms of a tuning-fork, as shown in Fig. 276,* — in which F\s one 
of the arms of the tuning-fork, and CAED a piece of elastic 
metal to which the stylus, AP, is attached, — and if the fork 
be put in vibration and the stylus permitted to come in contact 
with any surface that can be marked, as a smoked and var- 
nished cylinder moved at a uniform rate, the vibrations of the 
tuning-fork will be recorded on the cylinder by a series of 
wavy lines, as shown in Fig. 279; the distance between the 

*~See Thurston's Engine and Boiler Trials, page 233. 



§415-] METHODS OF TESTING THE STEAM-ENGINE. 575 

waves corresponding to known increments of time. If each 
revolution or portion of a revolution of the shaft whose speed 
is required be marked on the cylin- 
der, the distance between such marks, 
measured to the same scale as the 
wavy lines made by the tuning-fork, 
would represent the time of revolu- 
tion. 

Fig. 278 (from Thurston's Engine 
and Boiler Trials) represents the Ran- 
son chronograph ; in this case the tun- 
ing-fork is moved axially by a carriage 
operated by gears, and is kept in 

vibration by an electro-magnet. The operation of the instru- 
ment is the same as already described. The form of the 
record being shown in Fig. 279; the wavy marks being those 




Fig. 277.— Stylus for Tuning- 
fork. 




Fig. 278. — Tuning-Fork Chronograph. 

made by the tuning-forks, those at right angles being made at 
the end of a revolution of the shaft whose speed is required. 

The tuning-fork with stylus attached,* as in Fig. 277, can 
be made to draw a diagram on a revolving cylinder connected 



See Engine and Boiler Trials, page 234. 



576 EXPERIMENTAL ENGINEERING. [§ 4 J 7« 

directly to the main shaft of the engine, or the shaft itself 
may be smoked and afterward varnished. If the fork be 
moved axially at a perfectly uniform rate, the development of 
the lines drawn will be for uniform motion, straight and oi 
uniform pitch ; but for variations in speed these lines will be 




Fig. 279. — Speed-record from Chronograph. 

curved and at a varying distance apart. From such a diagram 
the variation in speed during a single revolution can be deter. 
mined. 

416= Autographic Speed-recorder. — Variations in speed 
are shown autographically in several instruments by recording 
on a strip of paper moved by clock-work the variation in cen- 
trifugal force of revolving weights. In the Moscrop speed- 
recorder, shown in Fig. 280, the shaft B is connected with the 
shaft whose speed is to be measured. The variation in the 
height of the balls near B, caused by variation in speed, gives 
the arm C a reciprocating motion, so that an attached pencil 
makes a diagram, FED, on the strip of paper moved by clock- 
work. The ordinates of this diagram are proportional to the 
speed. 

417. The Surface Condenser. — In the measurement of 
the steam used by the engine the surface condenser is fre- 
quently employed. The surface condenser usually consists of 
a vessel in which are a great many brass tubes. It is usually 
arranged so that the exhaust steam comes in contact with the 
outer surface of these tubes, and the condensing water flows 
through the tubes. The condensed steam falls to the bottom 
of the condenser and is removed by an air-pump ; the heat of 
the steam being taken up by the condensing water. If the 
condenser is free from leaks, the air-pump of ample size and 
with little clearance, and if the proper temperatures are main- 



§417-] METHODS OF TESTING THE STEAM-ENGINE, 577 

tained, nearly all the atmospheric pressure can be removed 
from the condenser and the back-pressure on the engine cor- 
respondingly reduced. 

The surface condenser affords more accurate means of 




Fig. 280 —The Moscrop Speed-recorder. 



obtaining the water-consumption of a steam-engine than the 
measurement of feed-water during a boiler-test, since the 
effect of steam-leaks are to a great extent eliminated. 

The condenser should be tested for leaks by noting how 



57 8 EXPERIMENTAL ENGINEERING. |_§ 418. 

long a given reading of the vacuum-gauge can be maintained 
when all the connecting valves are closed, or by turning on 
steam when the water-pipes are empty, or vice versa, and noting 
whether there is any leakage. 



FORM FOR TEST ON CONDENSER. 

Date 

Duration of test . . . . min. 

Barometer inches lbs. per sq. in. 

Temperature, entering steam C F. 

Temperature, condensed steam C , F. 

Temperature, cold condensing water C F. 

Temperature, hot condensing water C F. 

Hook-gauge reading (corrected) inches. 

(Hook-gauge reading) * 

Temperature at weir C F. 

Weight of condensed steam lbs. 

Breadth of weir inches. 

End area of tubes - sq. ft. 

Area steam surface sq. ft. 

Area water surface sq. ft. 

Weight steam condensed per hour lbs. 

Weight condensing water used per hour lbs. 

Weight steam condensed per pound of water .lbs. 

Weight steam condensed per sq. ft. steam surface per hour lbs. 

Weight steam condensed per sq. ft. water surface per hour lbs. 

Velocity of water through tubes ft. per sec. 

Heat acquired by condensing water used per hour B. T. U. 

Heat given up by steam condensed per hour. B. T. U. 

Signed , 

418. Calibration of Apparatus for Engine-testing.— 

Before commencing any important test, all instruments and 
apparatus to be used should be adjusted and carefully com- 
pared with standards, under the same conditions as in actual 
oractice. The errors or constants of all instruments should be 



§4 l8 -] METHODS OF TESTING THE STEAM-ENGINE. 579 

noted in the report of the test, and corresponding corrections 
made to the data obtained. 

The instruments to be calibrated are : 

1. Steam-gauge. — Compare with mercury column, or with 
standard square-inch gauge, for each five pounds of pressure, 
reading both up and down throughout the range of pressures 
likely to be used in the test. (See Article 282, page 366.) 

2. Steam-engine Indicat or -springs . — Put the indicator under 
actual steam-pressure (see Art. 393, p. 535) and compare the 
length of ordinate of the card with the reading of the mercury 
column or a standard gauge for the same pressure. Take ten 
readings, both up and down, through an extreme range equal 
to two and one-half times the number on the spring. The 
steam-pressure may be varied by throttling the supply and 
•exhaust. The ordinate may also be compared by a special 
method with readings of a standard scale ; the indicator being 
heated by the flow of steam through a rubber tube wound 
around it. 

3. Speed-indicators. — The accuracy can be checked by hand 
counting. For the best work chronographs should be used. 
Continuous counters are necessary for accuracy in a long run. 
(See Articles 414 and 415.) 

4. Indicator Reducing-motion. — This may be tested by divid- 
ing the stroke of the engine on the guides into twelve equal 
parts and noting whether the card is similarly divided. It 
should be tested for both return and forward stroke. When 
the form of the card is considered, this is an imports* matter, 
as many reducing-motions distort its shape. (See Article 390, 
page 528.) 

5. Indicator-cords and Connections. — See that the connecting 
cords do not stretch at high speeds, and that the drum-spring 
of the indicator has a proper tension and gives a correct motion 
of the drum. This is important. (See Article 395.) 

6. Weighing-scales. — Compare the readings with standard 
weights. 

7. Water-meters. — Calibrate by actually weighing the dis- 
charge under conditions of use as regards pressure and flow. 



580 



EXPERIMENTAL ENGINEERING. 



[§418 



In case meters are used, temperatures of the water must be 
taken in order to obtain the weight. (See Article 213, page 

283.) 

8. Thermometers. — Test the thermometer for freezing-point 
by comparison with water containing ice or snow ; test for boil- 
ing-point by comparison with steam at atmospheric pressure in 
the special apparatus described on page 381, the correct boiling- 
point being determined by readings of the standard barometer. 
The other tests of the thermometer can in general be left to 
the makers of the instrument. In cases where great accuracy 
is required the readings should be compared throughout the 
whole scale with a standard air-thermometer, as described on 
page 350. 

9. Pyrometer. — Compare with a standard thermometer 
while immersed in steam for the lower ranges of temperature, 
and with known melting-points of metals for higher. The 
correction may also be determined by cooling heated masses 
of metals in large bodies of water and calculating the temper- 
ature from the known relations of specific heats. (See Articles 
298 to 304). 

10. The Planimeter, which is used for measuring the indi- 
cator-diagram, should be calibrated by making a comparison 
with a standard area, as explained in Article 38, page 52. The 
following form is useful to record the results of calibrations : 



BLANK FORM FOR CALIBRATION OF INSTRUMENTS. 

Steam-engine Indicator-springs. 



Used on 


Head. 


Crank. 





































§ 4!9-] METHODS OF TESTING THE STEAM-ENGINE. 58 1 

Steam-gauges. 



Maker. 



Position. 



Number. 



Error, lbs. 



When Tested. 



How Tested. 



Thermometers. 



Position. 



Boiling-point. 



Registered 
Number. 



Read- Per Ba- 
ing. rometer. 



Error. 



Freezing-point. 



Read- 
ing. 



Error. 



Barometer. 



419. Preparations for Testing. — The preparations re- 
quired will depend largely on the object of the test. They 
should always be carefully made, and in general are to include 
the following operations : 

1. Weighing of Steam. — Prepare to weigh all the steam 
supplied the engine. This may be done by weighing or meas- 
uring all the feed-water supplied the boiler (see Article 375), 
provided there is no waste nor other use of steam ; or it may 
be done by condensing (see Article 417) and weighing all the 
exhaust from the engine. In the first case especial precaution 
must be taken to prevent leaks, and in the latter to reduce the 
temperature of the condensed steam to 1 io° F. before weigh- 
ing. The weights may in some cases be determined from a 
meter-reading (see Article 214). 

2. Quality of Steam. — Attach a calorimeter (see Articles 330 
co 336), which may be of the throttling or separator kind, to the 
main steam-pipe, near the engine. This attachment may be 
made by a half-inch pipe, cut with a long thread and ex- 
tending three fourths across the main steam-pipe. This pipe 



5 82 EXP E RIM EN TA L ENGINEERING. [§ 4 1 <>• 

should be provided with large holes so that steam will be 
drawn from all parts of the main steam-pipe (see page 370). 

3. Leaks. — The engine should be tested for piston-leaks by- 
turning on steam with the piston blocked and cylinder-cocks 
opened on the end opposite that at which steam is supplied. 
If leaks are found, they should be stopped before beginning 
the test. 

4. Indicator Attachments. — Arrange a perfect reducing-mo- 
tion. The kind to be used will depend entirely upon circum- 
stances. The lazy-tongs or pantograph is reliable for speed* 
less than 125, and can be easily applied. The pendulum piv- 
oted above and furnished with an arc, although not perfectly 
accurate, is much used. Make yourself familiar with the vari- 
ous devices in use. (See Article 390). 

5. An Absorption Dynamometer may be required ; if so, ar- 
range a Prony brake to absorb the power of the engine, and 
make provision for lubricating it and removing the heat gen- 
erated (see Article 178, page 528). In many commercial tests 
the power is absorbed by machinery or in useful work, and the 
efficiency is wholly determined by measurements of the amount 
and quality of steam and from the indicator-diagram. 

6. Weight of c^z/.-^-This is generally taken during an engine, 
test, but will be treated here as pertaining to boiler-testing ; 
the methods of weighing are fully described under that head 
(see Article 375). 

An engine fitted completely for a test is shown in Fig. 272,. 
from Thurston's Engine and Boiler Trials. In this case two 
indicators are employed, the drum-motion being derived from a 
pendulum reducing-motion; a Prony brake is attached to absorb 
and measure the power delivered, water for keeping the brake 
cool being delivered near the bottom and on the inside of the 
flanged brake-wheel by a curved pipe, and drawn out by an- 
other pipe the end of which is funnel-shaped and bent so as to 
meet the current of water in the wheel. The speed is taken by 
a Brown speed-indicator mounted on top of the brake, and also 
by a hand speed-indicator. The steam-pressure is measured 



§421.] METHODS OF TESTING THE STEAM-ENGINE. 583 

near the engine ; the quality of steam is determined by a sam- 
ple drawn from the vertical pipe near the engine. 

420. Measurement of Dimensions of Engine. — Make 
careful measurements of the dimensions of engine ; the diam- 
eter of piston, length of stroke, and diameter of piston-rod, 
as may be required. 

Piston-displacement. — This is the space swept through by 
the piston ; it is obtained by multiplying the area of the piston 
by the length of stroke. For the crank end of the cylinder 
the area of the piston-rod is to be deducted from the area of 
the piston. 

Clearance is the space at the end of cylinder and between 
valve and piston, filled with steam, but not swept through by 
the piston. To measure the clearance, put the piston at end 
of its stroke and fill the space with a known weight of water, 
ascertaining that no leaks occur by watching with valve-chest 
cover and cylinder-head removed. Make this determination 
for both ends of the cylinder, and from the known weight of 
water compute the volume required. 

This is usually reduced to percentage, by dividing by the 
volume of piston-displacement. 

This last reduction may be obviated, as suggested by Prof. 
Sweet, by finding, after the clearance-spaces are full of water, 
how far the piston will have to move in order to make room 
for an equal amount of water ; this distance divided by the full, 
stroke is the percentage required. Another approximate way 
sometimes necessary is to fill the whole cylinder and clearance- 
spaces with water ; from this volume deduct the piston-dis^ 
placement and divide by 2. 

Preliminary Run. — It will be found advisable to make a pre- 
liminary run of several hours before beginning the regular 
test, to ascertain if all the arrangements are perfect. 

421. Quantities to be observed. — The observations to be 
taken on a complete engine-test are given in the following 
list. 

Fill out the following blank spaces. 



5 8 4 



EXPERIMENTAL ENGINEERING. 



t& 422. 



Kind of engine 

Maker's name 

Brake-arm feet. 

Diameter cylinder inches. 

Length stroke feet 

Diameter piston-rod inches. 

Diameter crank-pin " 

Length crank-pin " 

Diameter wrist-pin " 

Travel valve " 



DESCRIPTION OF ENGINE. 

Lap of valve inches. 

Scale indicator-spring 

Piston area sq. in. 

Steam-port area " 

Exhaust-port area " 

Diameter fly-wheel inches. 

Clearance, head lbs. water. 

crank " " 

per cent P.D. head 

" " " crank 



Number 

Time 

Revolutions : 

Continuous counter 

Speed-indicator 

Gauge-readings : 

Boiler lbs. 

Steam-pipe " 

Steam-chest ** 

Exhaust .inches hg. 

Condenser " " 

Barometer " '* 

Temperatures : 

External air 



LOG Of TEST. 

Temperatures 



Engine-room 

Condensed steam, 

Feed-water 

Injection-water.. . 
Discharge- water. . 
Calorimeter : 

Steam-pipe 

Steam-chest 

Weights : 

Condensed steam. 

Feed-water 

Injection-water. . . 
Calorimeter.. 



422. Special Engine- tests.— Preliminary Indicator Prac- 
tice. — A simple test with the indicator will be found a 
useful exercise in rendering the student familiar with the 
methods of handling the indicator and of reducing and conv 
puting the data to be obtained from the indicator-diagrams 
The directions are as follows : 

Apparatus. — Throttling calorimeter ; steam-gauge ; two indi' 
cators ; reducing-motion, and indicator-cord. 

1. Obtain dimensions of engines. Measure the clearance \> 
see that indicators are oiled and in good condition, and that 



§ 422.] METHODS OF TESTING THE STEAM-ENGINE. 585 

the reducing-motion gives a perfect diagram. Adjust the 
length of cord so that the indicator will not hit the stops. Pre- 
pare to take cards as explained in Article 398, page 545. 

2. Take diagrams once in each five minutes, simultaneously 
from head and crank end of cylinder ; take reading of boiler- 
gauge, barometer, gauge on steam-pipe or on steam-chest, 
vacuum-gauge if condenser is used, temperature or pressure of 
entering steam, temperature of room, and number of revolu- 
tions. 

3. Measure or weigh the condensed steam during run. 

4. From the cards taken compute the M. E. P. and I. H. P. 
for each card as. required by the log. 

5. Take a sample pair of diagrams, one from head and one 
from crank end. (a) Find clearance from diagrams (see Article 
407, page 561) ; (b) draw hyperbolae respectively from cut-off and 
release and find re-evaporation and cylinder condensation (see 
Article 408) ; (c) produce hyperbola from release to meet hori- 
zontal line- representing boiler-pressure; complete the diagram 
with hyperbola from point of admission. Compute the work 
(I. H. P.) from this new diagram. Draw conclusions from the 
form of card (see Article 409). 

6. Compute the steam-consumption per stroke and per 
I. H. P. at cut-off and at end of stroke from the diagram (see 
Article 406). Compare this with the actual amount as deter- 
mined by the test. 

7. From the weight of dry steam as shown by the indicator- 
diagram, and the actual weight as determined by the amount 
of condensed steam, determine the quality at cut-off and re- 
lease. 

8. Make report of test on the following form : 

REPORT OF TEST ON ENGINE. 

Date 

Duration of test ....=... min. 

Revolutions per min 

Steam used per min. c lbs 

Barometer. in " 



586 



EXPERIMENTAL ENGINEERING. 



[§ 423. 



Piston-displacement 

Clearance (per cent of P. D.) 

Engine constant 

Cut-off (per cent of stroke) 

Release (per cent of stroke) , 

Compression (per cent of stroke). 

Pressure at cut-off 

Pressure at release 

Pressure at compression , 

Mean effective pressure 

Revolutions per minute 

Horse-power , 



Crank End. 
cu. ft. 



lbs. 



Head P.nd. 
cu. f t 



lbs. 



C. E. 



H. E. 



Per Stroke. 



C. E. 



H. E. 



Per Revo- 
lution. 



.Total. 

Per 

I.H.P. 



.lbs. 



Weight of steam at cut-off 

Weight of steam at release 

Weight of steam during compression. . . 

Re-evaporation per H. P. per hour 

Weight of water per revolution, actual '* 

Weight of mixture in cylinder per revolution " 

Per cent of mixture accounted for as steam at cut-off 

Per cent of mixture accounted for as steam at release 

Weight of water per H. P. per hour, actual lbs. 

Weight of water per H. P. per hour, by indicator " 

Signed. 

423. Valve-setting. — This exercise will consist, first, in 
obtaining dimensions of ports and valves, and in drawing the 
valve-diagram corresponding to a given lead and angular ad- 
vance, and setting the valve by measurement with a lead cor- 
responding to that shown on the diagram. The valve-diagram 
may be drawn by Zeuner's * or Bilgram's method, as may be 
convenient ;f from the valve-diagram draw the probable in- 
dicator-diagram and compute its area, and from that figure 
the indicated horse-power.:): 

* See Valve-gears, by Halsey. D. Van Nostrand Co., N. Y. 
f Valve-gears, by Peabody. J. Wiley & Sons, N. Y. 
\ Valve-gears, by Spangler. J. Wiley & Sons. N. Y. 



§ 4 2 3-] METHODS OF TESTING THE STEAM-ENGINE. 587 

The method of drawing the indicator-diagram by projection 
from the valve-diagram is well shown in Fig. 281, from Thurs- 
ton's Manual of the Steam-engine. The steam-pressure and 
back-pressure lines being assumed, the various events as shown 
on the valve-diagram are projected upon these lines, and the 
indicator-diagram completed as shown. 

Secondly, in attaching the indicators and taking diagrams 




v Point of 
* T Admission 



Fig. 281.— Indicator-diagram constructed from Valve-diagram. 



from which the error in the position of the valve is determined. 
Its position is corrected as required, to equalize the indicator- 
diagrams taken from each end of the cylinder. 

The special directions are as follows : 

Apparatus. — Scale, dividers, and trammel-point, the latter 
consisting of a rod the pointed end of which can be set on a 
mark on the floor and which carries a marking point at the 
other end. 

I. Measure dimensions of valves and ports, throw of ec- 
centric, and other dimensions called for by engine-log. 



588 EXPERIMENTAL ENGINEERING. [§ 423, 

2. From these data, with a definite lead assumed, draw 
valve-diagram, and note position of piston for cut-off, release, 
compression, and admission. 

3. Set the valve to the assumed lead, and with angular ad- 
vance as indicated by the valve-diagram. Turn the engine 
over and see that the lead is the same at both ends of the 
cylinder. 

This requires the engine to be set on its centre ; this is 
done by bringing the piston to the extreme end of the stroke 
at either cylinder-end, so that the piston- and connecting-rods 
form one straight line. As the motion of the piston is very 
slow near the end of the stroke, this position is determined 
most accurately as follows : Mark a coincident line on cross- 
head and guides corresponding to the position of the crank 
when at an angle of about 20 measured from its horizontal 
position ; then, from a fixed point on the floor, swing the 
trammel-point as a radius, and mark a line on the circumference 
of the fly-wheel ; turn the engine over until the marks again 
coincide with the crank on the other side of the centre and 
make a second mark on the fly-wheel with the trammel-point; 
bisect the distance on the wheel between these marks and ob- 
tain a third line ; turn the wheel until this line is shown by the 
trammel to be at the same distance from the reference-point, 
on the floor, as the other marks: the engine will then be on 
its centre. Move the valve the proper amount to make its 
position correspond with that shown on the diagram. In set- 
ting the valve remember that to change angular advance, the 
eccentric must be rotated on the shaft ; and to equalize events 
for both ends of cylinder, the valve must be moved on the 
stem. These adjustments must be made together, as they are 
to some extent mutually dependent. 

4. From the valve-diagram draw an ideal indicator-diagram 
as explained, assuming initial steam-pressure to be (a) pounds 
per square inch, absolute back pressure 5 pounds absolute, and 
that expansion and compression curves are true hyperbolae. 

Calculate its area by formula. 

Area = PV{i + \og e r) - P V (i + log e r'), 






§ 4 2 5-] METHODS OF TESTING THE STEAM-ENGINE. 589 

in which V = volume at cut-off, and P ■— corresponding pres- 
sure ; V = clearance volume, and P = clearance pressure ; 
r = number of expansions, and r' = number of compressions. 
5. Compute the horse-power of the diagram so drawn, and 
compare with that shown by the diagram taken. 

424. Friction-test. — For this test the engine should be 
fitted with a Prony brake (see Article 169, page 239, to absorb 
and measure the power developed. Indicator-diagrams are 
to be taken and the indicated horse-power computed (see 
Article 402, page 552). The indicated horse-power being the 
work done by the steam on the piston of the engine, the dyna- 
mometer horse-power, that delivered by the engine, the dif- 
ference will be the power absorbed by the engine in friction, 
or the friction horse-power. It is customary to reduce this 
amount to equivalent mean pressure acting on the piston by 
dividing by product of area of piston in square inches and 
speed in feet per minute. In making the test for friction of 
the engine the loads on the brake-arm should be varied, with 
the speed uniform, or the load on the brake-arm should be 
constant with varied speed, noting in each case the effect 
on the frictional work. It has been shown by an extended 
series of experiments * that the friction of engines is practically 
constant regardless of the work performed, and that the work 
shown by the indicator-diagram, when the engine is running 
light or not attached to machinery, is practically equal to the 
engine-friction in case the speed is maintained uniform. In 
the case of variation in speed the friction work increases nearly 
in proportion to increase of speed. 

Detailed directions for this test are not considered neces- 
sary. 

425. Simple Efficiency-test. — Engines are frequently 
sold on a guarantee as to coal or water consumption per in- 
dicated horse-power (I. H. P.), or in some instances per dyna- 
mometer horse-power (D. H. P.); in such a case a test is to be 
made showing the I. H. P. or the D. H. P. as may be required, 
and the water and coal consumed. 

* See Transactions Am. Soc. Mech. Engineers, Vol. VIII., page 86. 



590 EXPERIMENTAL ENGINEERING. [§ 426. 

The I. H. P. is to be obtained as already explained in 
Article 402 ; the D. H. P. by readings from a Prony brake, 
Article 178. The coal-consumption is to be obtained by a 
boiler-test, Article 375 ; the total water consumed, by the feed 
water used in the boiler-test, corrected for leaks and quality; 
or by condensing the steam in a surface condenser, Article 417, 
The quality of the steam should be taken near the engine, as 
explained iiv Article 336, page 433. The principal quantities 
to be observed are quantities required for a boiler-test, quality of 
steam near engine, number of revolutions of engine per minute, 
and weight of feed-water or weight of condensed steam. These 
observations should be taken regularly and simultaneously 
once in ten or fifteen minutes, and at the same instant an in- 
dicator-diagram should be taken. From these data are com- 
puted the quantities required. 

426. The Calorimetric Method of Engine-testing.— 
Hirris Analysis. — The calorimetric method of testing engines 
as developed from Hirn's theory by Professor V. Dwelshauvers- 
Dery of Liege enables the experimenter to determine the 
amount of heat lost and restored and that transformed into 
work in the passage of the steam through the cylinder.* 

The principle on which the method is founded is as follows: 
The amount of heat supplied the engine is determined by 
measuring the pressure, quality, and weight of the steam ; that 
removed from the engine is obtained by measuring the heat in 
the condensed steam and that given to the condensing water. 
The amount of heat remaining in the cylinder per pound of 
steam at any point after cut-off can be calculated from the data 
obtained from the indicator-diagram ; this multiplied bij the 
known weight gives the total heat. 

The heat supplied to the engine added to that already 
existing in the clearance-spaces gives the total amount of heat 
available ; if from this sum there be taken the heat existing at 
cut-off and the heat equivalent of the work done during 
admission, the difference will be the loss during admission, due 

* See Table Properties of Steam, V. Dwelshauvers-Dery, Trans. Am. Soc. 
M. E., Vol. XI. 



§ 4 2 6.] METHODS OF TESTING THE STEAM-ENGINE. 59 1 

principally to cylinder-condensation. The difference between 
the heat in the cylinder at cut-off and that at release after de- 
ducting the work equivalent is that lost or restored during 
expansion. This method applied to all the events of the 
stroke, and at as many places as required, gives full informa- 
tion of the transfer of heat to and from the metal. 

In the fundamental equations of this analysis which follow, 
the following symbols are used : 



Quantity. 


Symbol. 


Quantity. 


Symbol. 


Heat admitted per stroke. . . . 
Weight of steam per stroke. . . 
Absolute pressure of entering 

steam, per sq. inch 

Temperature, degrees Fahr. 
Heat of the liquid ........... 


Q 

M 

P 
t 

? 
P 
r 

X 

D 

I — X 

c P 


Heat equivalent of energy of 
steam in the cylinder at any 
instant 


h 


Joule's equivalent 

Reciprocal of Joule's equiva- 
lent 


J 

A 




Weight of 1 cu. foot of steam. 

Vol. of r lb. of steam, cu. ft. . 

Volume of cylinder to any 
point under consideration 
moved through by the piston, 
cu. ft .' 


§ 


Total latent heat 
















Specific heat of steam of con- 


v 


Volume of clearance, cu. ft. . . 
External work in foot-pounds. 
Vol. of 1 lb. of water in cu. ft . 


w 

a 





The value of the quantity at any point under discussion i c 
denoted by the following subscripts : clearance, c ; beginning of 
admission, o ; cut-off, 1 ; release, 2 ; beginning of compression. 

The equations are as follows for wet or saturated steam ': 
Heat in the Entering Steam. — 



Q=M(a+xr); 



(I) 



if the steam is superheated D degrees, 



Q = M{q+r+c t D). 



(2) 



592 EXPERIMENTAL ENGINEERING. [§426. 

Heat in the Cylinder. — Since the steam in this case is in- 
variably moist, we have the following equations : 

In the clearance spaces, h c = M (g c -\- x c p c ) ; ... '3) 

At admission, k = M (g + x p ) ; . . . (4) 

At cut-off, K = (M+M,)(q, + x lf >,)', . (5) 

At . elease, h, = (M + M )(g, + x A ) ; . (6) 

At compression, h % — M (<? 3 + x s p t ) . ... (7) 

The external work is to be determined from the indicator- 
diagram. Let the heat equivalent of this work be represented 
as follows: 

During admission, AW a \ (8) 

During expansion, AW b ; (9) 

During exhaust, AW C \ (10) 

During compression, AW d . . . . . . . . . (11) 

The volume in cubic feet, V, of a given weight of steam, 
My can always be expressed by the formula 

V=M(xu+o); ...... (12) 

in which u equal the excess of volume of one pound of steam 
over that of one pound of water ; u — v — a. 

Substituting the value of u in the above equation, 

V=M(xv+<r(i-x)) (13) 

As cr is a very small quantity, (1 — x)<r can be safely 
dropped as less than the errors of observation, and in all prac- 
tical applications the formula used is 

V— Mxv (14) 



§ 426.] METHODS OF TESTING THE STEAM-ENGINE. 593 

In the exact equation (13) or the approximate equation 
(14), if the pressure, weight, and volume of steam are known, 
its specific volume, v, can be found, and x may be computed. 

At any point in the stroke after the steam-valve is closed, 
the volume and pressure of steam in the cylinder can be 
determined from the indicator-diagram if the dimensions of 
the engine and its clearance are known. If the weight of steam 
used is known from an engine-test, there can be determined 
from the indicator-diagram both the quality and amount of 
heat in the cylinder at any point, with the single exception of 
the steam remaining in the clearance spaces. Thus let V e 
equal volume of clearance; V -f- V c , volume at admission, 
usually equal to V c ; V x -{- V ei volume at cut-off ; V 7 -f- V c , at 
release ; V % -f- V c , at compression ; M, the weight of steam 
used ; M , the weight of steam caught and retained in the 
clearance spaces. Then, by method used in equation (12), 

V c = M£x c u c + <r e ); (15) 

V +V c = M (x oK +<r ); (16) 

K+r^iJf.+JfXx^+aJ; . . . (17) 

V,+ V c = (M + M)(x,u 2 +cr 2 ); . . . (18) 

r t +K = M.{x t u t + <rJ (19) 

In the above equations we know the volumes and pressures 
for each point, and the weight of steam, M, passing through 
the engine. So that in the five equations there are six un- 
known quantities : M , x CJ x Q , x x , x 2 , and x z , of which x may 
be assumed as 1.00 without sensible error. In the above equa- 
tions, (15) and (16) are usually identical ; they differ from each 
other only when there is a sensible lead which shows on the 
diagram. 

The weight of steam in the clearance space is computed 
from equation (15): 

M* =(V £ ) + {x c u c + <r e ) = V c -T- x c v ( , nearly. 



594 EXPERIMENTAL ENGINEERING. [§ 426. 

Assume x = 1.00: 

M =V e -T-v e . (20) 

In computing the heat at any point, it is customary to com- 
pute the sensible and internal heat in two operations. Thus 
in equation (4) make k, the total heat, equal to H, the sensible 
heat, plus H ', the internal heat ; then 

or H,= M,q, (21) 

H:=x,p,M a ; (22) 

and in equation (5), 

H x = qiM a + M), ........ (23) 

H; = {x lPl ){M + M). . (24) 

From equation (17), 

M, + M=Z±Zi= *+*■ ,-£±3, nearly. (25) 

By substituting in (24), 

if/^PXK+vj + vr, 

which form is used in the computations that follow. 

The analysis determines the loss of .heat during a given 
period, by rinding the difference between the heat in the cylin- 
der at the beginning of the period and the sum of that utilized 
in work during the period and that remaining at the end of 
tb.e period. 

The following directions and example should make the 
method clearly understood. 



§ 427.] METHODS OF TESTING THE STEAM-ENGINE. 595 

The total heat received and discharged per stroke is obtained 
by testing. The distribution of the heat and its relations to the 
work performed is obtained by measurements from the indicator 
diagram. For this purpose the diagram is divided as indicated 
in Fig. 282, so that the mechanical work for the respective periods 
of admission, expansion, release, and compression can be com- 
puted. The heat received at the beginning and discharged a; 
the end of each of these periods is compared with the mechanical 




Fig. 282. — Diagram from a Greene Engine. Cylinder, 26 inches in diameter by 
36 inches stroke. boiler-pressure, 80 revolutions per minute. scale, so. 



work expressed in heat-units done during that period. From 
this comparison the amount of heat interchanged, plus or minus, 
is computed for each period. It is to be noted that work done on 
the forward stroke is positive and that on the back stroke negative. 

427. Directions for Engine-testing by Hirn's Analysis. 

Directions. — 1. Make a complete engine- test with a constant 
load, weigh the condensing water, and measure its temperature 
before and after condensing the steam. Obtain the quality of 
the entering steam either in the steam-pipe or steam-chest; if 
convenient, make calorimetric determinations of the quality of 



596 EXPERIMENTAL ENGINEERING. [§ 427. 

the steam in the exhaust, which may be used as a check on the 
results, but which is necessary in case the exhaust steam is 
not condensed. 

2. Calibrate all the instruments used, and correct all obser- 
vations where required. 

3. From the average quantities on the log, corrected as 
shown by the calibration, fill out form I, of data and results. 
The steam and condensing water used per revolution to be di- 
vided between the forward and backward strokes of the piston 
in proportion to the M. E. P. of these respective strokes, as 
shown on the log. 

4. Draw on each diagram as explained lines corresponding to 
zero volume and to zero pressure, and divide the diagrams as 
shown in Fig. 226 into sections, by drawing lines to points of 
admission W, cut-off en, release Oe, and compression od. 

Measure for each diagram the percentages of cut-off, release, 
and compression, calling the original length of the diagram 
without clearance 100 per cent. 

5. Measure the absolute pressure from each card and enter 
the averages in blank form No II, using subscripts as follows: o, 
admission ; 1, cut-off ; 2, release ; 3, compression ; c, clearance. 

Take from a steam-table the heat of liquid, internal latent 
heat, total latent heat, total heat, and specific volume, corre- 
sponding to each of the above pressures. 

6. Compute the volumes in cubic feet for clearance, total 
volumes, including clearance, at admission, cut-off, release, and 
compression, and place the average results in the proper 
columns. 

7. Compute the area corresponding to each period into 
which the diagram is divided and find the mean pressure for 
that period. Also find the work done in each period, expressed 
in foot-pounds and also in B. T. U. (It is to be noted that the 
work done during the return stroke is negative.) Enter the 
average of these results in the proper place, noting the use of 
the subscripts a, b, c, and d. 

8. Calculate the heat-losses as indicated on Form III, which 
is an account of the heat used during 100 strokes of the engine. 



§ 4 2 7*] METHODS OF TESTING THE STEAM-ENGINE. $g? 

The weight of steam, M, in pounds is ioo times the amount used 
for one stroke as given on Form I. The weight of steam in 
clearance is to be calculated for admission, pressure, and volume, 
and with x equal i.oo. M , to be calculated in the same manner. 
Calculate from known weights and temperatures the heat ex- 
hausted from the engine in the condensed steam K! and in the 
condensing water K. 

Calculate by the formulae, as explained, the heat supplied 
the engine, and the sensible and internal heat, at each event in 
the stroke of the engine. 

9. Calculate the cylinder-loss at admission as the difference 
between that supplied added to that already in the clearance, 
and that remaining at cut-off added to that used in work. If 
the heat is flowing from the metal, the sign will be negative, 
otherwise positive. 

10. Perform the same operation for each period of the 
engine ; the difference between the heat at the beginning of 
each period and that at the end, taking into account the work 
done, is the loss. 

11. Take the algebraic sum of these losses and of the heat 
equivalent of the external work, and if no error has been made 
in the calculations, this sum, which is the total transformation, 
will equal the difference between the heat supplied and that 
exhausted. That is, using the symbols of the analysis, D = D! 
It is also evident that this quantity is the loss by radiation. 

The importance of this check on the accuracy of the com- 
putations should not be overlooked. If no errors of computa- 
tion are made, in each case the value of D will equal that of D f . 

12. Make the remaining calculations as on Form IV; these 
give the quality which the steam must have at various portions 
of the stroke to correspond with the foregoing calculations. 
The quality is calculated from the volume remaining in the 
cylinder. Compute the various efficiencies. 

Note that the heat lost during admission is in some respects 
a measure of the initial cylinder-condensation. 

The following forms are given partially filled out with the 
results of a test made by application of Hirn's analysis. 



59 8 



EXPERIMENTAL ENGINEERING. 



[§ 428. 



428. Forms for Hirn's Analysis. 



Si 









vSuudg jo 3[bds 






2 
pq 


d 'H a 






•pBoq 






•i^ox -a -h 1 






M 

C 
rt 

u 

i 


d'H I 






•d a h 






d H "I 






"d a/K 






05 

."3d 
*S 

(0 

u 

u 
3 
rt 
<u 

a 

a 

H 








•jajBM-uoiioafuj 






•J3JBM-P33J 






•raBais pasaapuo^ 






u 

s 

'C 

"rt 
U 


•jsriBqxg 






•japing 




Cfl 

W 


•;S3t[3-UIB93S 




to 


•3dxd-uiB3ig 




O 
O 


•J35BM-3SjBl{0SIQ 


O 


•J3JBA4.-U0I133CUI 1 




•aajBM-paa^ 1 




•UIB3JS pasuapao3 






•niooj-auiSaa i 




•jiy iBUJajxg 




«5 

c 
■3 

rt 
1 

V 

be 

3 

rt 



en 
<U 

.3 
o 

3 


•jaiaraoJBg 




•J3SU3pU03 




'}snBqxg 






c 
s 
o 


•qsaqD-raBajs 




•adid-uiB3is 1 




•aaiiog 






-r? en 
> 


•iojBoipni-paads 






•jaianoo snonupuo3 






•3TOIX | 








uaqtanM 





afl 



W Oh 



TO _C 

55 W 



6 



in 

V jj , n 

« a • g | £ 

_ ""* .5 *** 

o .S a .5 aT .S 

§ -* c «- rt 



OT ™ *- »- ^- rt 

s* b% e 1 2" 

cd rt c cs rt a* 

._, .-, v ;~ <-■ rt 

Q Q J Q H a 



U 



c o 



rt ctj C 
I* .— u 

PQ D J 



§ 4 28 -J METHODS OF TESTJNG THE STEAM-ENGINE. 599 

Form No. I. 

APPLICATION OF HIRN'S ANALYSIS TO SIMPLE CONDENSING 

ENGINE. 
Data and Results. 

Test of steam-engine made by . at Cornell University, 

Kind of engine, slide-valve throttling. Diameter cylinder 6.06 inches. 

Length stroke 8 inches. Diameter piston-rod. . i^f " 

Volume cylinder crank end, o. 12921 cu. ft. ; head end, o. 13354 cu - ft* 

Volume clearance, cubic foot, head 0.01744 

Clearance in per cent of stroke 13.06 

Volume clearance, cubic foot, crank 0.01616 

Clearance in per cent of stroke 12.51 

Boiler-pressure by gauge 69.4. Barometer 29.276 

Boiler pressure absolute, pounds 83.7 

Boiling temperature, atmospheric pressure, deg. F 210.7 

Revolutions per hour 11898 

Steam used during run, pounds 716.424 

Quality of steam in steam-pipe 0.99 

Quality of steam in steam-chest 0.9941 

Quality of steam in compression 1.001 

Quality of steam in exhaust 0.9021 

Weight of condensed steam per hour = . . . . 259.92 

Pounds of wet steam* per stroke head, 0.0109707; crank, 0.0109383 

Temperatures condensed steam 103.47 deg. F. 

Temperatures condensing water cold, 42.758 deg. F.; hot, 92.219 * 

Pounds of condensing water, per hour 5044.878 

" " " " " revolution 0.42429 

" " " " " stroke-head 0.212016 

'* " " " " crank 0.212274 

Symbols. 
To denote different portions of the stroke, the following subscripts are used: 
Admission, a; expansion, b; exhaust, c; compression, d. 

To denote different events of the stroke, the following sub-numbers are used* 
Cut-off, 1; release, 2; compression, beginning of, 3; admission,, beginning of, 
0; in exhaust, 5. Quality of steam denoted by X. 

Cut-off, crank end, per cent of stroke. . . 20.544. Release, crank end. . 93.95$ 
Cut-off, head end, per cent of stroke... . 18.963. Release, head end. . . 94.971 

Compression, crank end, per cent of stroke 52.341 

Compression, head end, per cent of stroke 39-77<> 

Pounds of steam per I. H. P 39-351 

Pounds of steam per brake H. P 55.314 

I. H. P.- Head 3-3152. Crank 3-3Q54- Total 6.6206 

Brake horse-power 4. 71 

* Wet steam is the steam uncorrected for calorimetric determinations. 



6oo 



EXPERIMENTAL ENGINEERING. 

Form No. II. 



[§ 428. 



ABSOLUTE PRESSURES FROM INDICATOR-DIAGRAMS AND 
CORRESPONDING PROPERTIES OF SATURATED STEAM. 





Cut-off. 


Release. 


Beginning 


Symbols. 




Com- 
pression. 


Of Ad- 
mission. 


Ran- 
kine. 


Clau- 
sius. 


Subscripts used 


I 


2 


3 





P 

s 

I 

L 

H 

C 

K 




a u i S Head 
Absolute pressure. . -j Crank 

Heat of liquid j g^ 

Internal latent heat, j c , a a nk 












P 


















1 














9 


Latent-heat evapo- j Head 
ration ( Crank 




















To-, heat | &* 

Vo.. I lb.cu.£,...j«- d k 




















A 






















K+r> 


V c +Vs 


^c+^3 


^o+F c 





































MEAN PRESSURES AND HEAT EQUIVALENTS OF EXTERNAL 

WORK. 





i/i 

.2* 
"C 
u 

CO 

£> 
3 
(A 


Head End. 


Crank End. 




Mean 
Pressures. 


External Work. 


Mean 
Pressures. 


External Work. 




Foot-lbs. 


B. T. U. 


Foot-lbs. 


B. T. U. 


Symbols 


a 
b 
c 
d 


MP 


w 


AW* 


MP 


W 


A IV* 


Admission, 

Expansion. ...... 




























Compression 

Total 











































* A = ij-fr . V c = volume in clearance-spaces. 



§ 4 2 8.] METHODS OF TESTING THE STEAM-ENGINE. 6oi 



tv 00 00 



I I 



O »0 t-» d 



rn t^« m m 



h m rr, os (r) pi (« 
JO CO o « 00 00 

I I I " 



J* 



-s- ^° 


AfcT 


>^ 


sT 


T+ + 


£*3 + 


6"^ + 


" + 


£ H <S ^ 


+ fcT 


+ 1° 


Sk° 


w fc- *« 


i * 


I * 


i * l 



I I 



i 

T i 

i i 
j j 
+ 



^ + 

+ + 
-1- i + 



0»«3 It; U; t< Oj Oi 






a; Uj oj a; a; a; ^ o* 0* Oj c» <*> c> Ci, 



s 

^ >- e 
« 4) S 



« -2 



S "2 rt S 

g « i o 

° w o o 

£ rt *t<~ 

a s a 2 

rt rt rt rt 

u u t> v 



•o ,_, j. 

.2 rt 13 

£•3- - 

! g'l g 

CO rt 3 5 

« 4; r* *e 



8 (H 

rt o CJ u »- 

rt rt rt co rt 



1 II II 

T3 X X O 3 

rt u u u 



So '3c ■- 

2 « j= 



-3 « "= 



Cn in X V X X m 



S 8 8 

ffi hJ hJ 



o 
c t> 

*£? 

85 rt 

~ J3 

rt cj 
3.2 

(WO 

£* 



602 



EXPERIMENTAL ENGINEERING. 



L§ 428. 



c 
o 



a 



r^ a> >o 00 



V 


^ L . 


<? 


s « 


4) k w 

rt ^ 
u 






2 + 


I \ 


\ \ 


r 1 


1 VL 



■ f + + 



« JS o -O \ I 00 ' I T ' K 






« ►* v. M 



§ % 



«**•■« 



a 



8 1 



a a - - 



2 £ "3 



o 6 a 

♦3 T3 rt 



<~ <+H ,0 



1= ^r *o 



O J" «J o tj o 



a 



rt rt rt rt ^ 

•V <U <V <U V 



v rt rt j3 
ffi « Pi H 






</) rt 

a a 



§ 43°-] METHODS OF TESTING THE STEAM-ENGINE. 603 

429. Hirn's Analysis applied to Non-condensing En- 
gines. — In this case: I. Determine the weight of water used 
by weighing that supplied the boiler, taking precautions to 
prevent loss of steam between the engine and the boiler by 
leaks. Apply the calorimeter and ascertain the quality near 
the engine. The heat in one pound of steam above 32 Fahr. 
will be represented by the formula xr -f- q, as previously 
explained. This quantity multiplied by the weight, M y is the 
heat supplied. M may be taken for 1 or for 100 strokes, as 
convenient. 

2. Determine the quality of the exhaust-steam by attaching 
a Calorimeter in the exhaust-pipe, close to the engine. The 
heat discharged by one pound will be, as explained in Article 
III, x e r e -\- q e \ in which the symbols denote quantities taken 
at exhaust-steam pressure. This quantity multiplied by the 
weight, M, is the heat discharged, and is equal to K -{- K' in 
the Form III, page 543. 

3. With these exceptions, the method is exactly as explained 
for the condensing engine, and the same forms are to be used. 

In obtaining the quality of the exhaust-steam, a separating 
calorimeter (see Art. 337) through which the steam is drawn 
by suction, can be used with success. 

430. Application of Kirn's Analysis to Compound 
Engines. — Compound engines are usually run condensing, and 
the special directions are for that case ; but in case the engine 
is run non-condensing the method of Article 429 can be applied. 

Directions. — With calorimeter between the cylinders : 

1. Attach a calorimeter in the exhaust of the high-pressure 
cylinder, and determine the heat exhausted from the high- 
pressure cylinder as explained for non-condensing engines. 

Treat the high pressure cylinder as a simple non-condensing 
engine, as explained in Article 429. 

2. Determine by the calorimeter between the cylinders the 
heat supplied to the low-pressure engine. This quantity will 
be the same as that exhausted from the high-pressure, corrected 
for steam used by the calorimeter and for radiation from the 
connecting pipes. 



604 EXPERIMENTAL ENGINEERING. [§ 43 1 

3. Fill out the forms for each cylinder as a separate engine. 

By using two calorimeters between cylinders the same 
method can be applied to a triple-expansion engine. 

In case the pressure of the steam between the cylinders is 
less than atmospheric a calorimeter can be used by attaching a 
special air-pump and condenser, so as to secure a flow of steam 
through the calorimeter. 

Without calorimeter between the cylinders : 

1. Determine the weight of steam, M, for both cylinders 
from the condensed steam of the low-pressure cylinder. This 
will give the quantity M. 

2. For the high-pressure cylinder compute the quantities 
as in Form III, omitting those terms containing AT and K\ the 
heat exhausted. 

3. Determine K and K' as follows: K -\- K' is evidently 
equal to the heat supplied the high-pressure engine, less the 
heat transformed into work, expressed in B. T. U., less the loss 
by radiation. The total loss by radiation in the whole engine 
is equal to the heat supplied the first cylinder, less the work 
done by all the cylinders, less the heat discharged from the last 
one. As an approximation, divide this total radiation-loss 
equally between the cylinders, assuming that the lower tem- 
perature of the low-pressure cylinder will offset its increased 
size. This will give us in Form III the value of D = Q — B. 
Compute B, substitute this value in the equation B = K + 
K' -\- AW. Compute K -f- K! and complete the analysis for 
the high-pressure cylinder. 

4. For the low-pressure cylinder, determine the entering 
heat as that discharged from the high-pressure cylinder, K-\-K ', 
plus the assumed radiation as given above. 

Make a complete analysis for each cylinder as explained for 
a simple engine. 

431. Hirn's Analysis applied to a Triple-expansion En- 
gine. — When the quality of the steam between the cylinders 
can be determined, treat the engine as three separate engines 
as explained. 



§43 r -] METHODS OF TESTING THE STEAM-ENGiNE. 605 

When the quality cannot be determined, treat the case as 
explained for a compound engine, as follows : 

1. Find the entire loss as equal to the difference between 
that supplied to the first cylinder and that discharged from the 
last, increased by the work done in the whole system reduced 
to thermal units. Divide this by the number of cylinders to 
find the assumed radiation-loss from each. 

2. Take the cylinders in series, and assume the discharged 
heat to equal the heat supplied, diminished by that transformed 
into external work, and make a separate analysis for each 
cylinder as explained for a simple engine. 

The following is an application of Hirn's analysis to a 
triple-expansion engine by Prof. C. H. Peabody at the Massa- 
chusetts Institute of Technology. 

The main dimensions of the engine are as follows : 

Diametev of the high-pressure cylinder 9 inches. 

Diameter of the intermediate cylinder 16 " 

Diameter of the low-pressure cylinder 24 " 

Diameter of the piston-rods 2 r ^ " 

Stroke 30 " 

Clearance in per cent of the piston displacements : 

High-pressure cylinder, headend, 8.83; crank end, 9.76 

Intermediate " 10.4 " 10.9 

Low-pressure " " 11.25 " 8.84 

The following table gives the data and results of a test 
with Hirn's analysis, made by the graduating class: 

Duration of test, minutes 60 

Total number of revolutions 5299 

Revolutions per minute 88.3 

Steam-consumption during test, pounds: 

Passing through cylinders 1193 

Condensation in high-pressure jacket 57 

" in first receiver jacket 61 

in intermediate jacket 85 

s ' in second receiver jacket 53 

in low-pressure jacket , 89 

Total 153a 



606 EXPERIMENTAL ENGINEERING. [§ 431- 
Condensing water for test, pounds 22847 

Priming, by calorimeter 0,013 

Temperatures, Fahrenheit; 

Condensed steam 95.4 

Condensing water, cold 41.9 

Condensing water, hot 96. 1 

Pressure of the atmosphere, by the barometer, lbs. per sq. in 14.8 

Boiler-pressure, lbs. per sq. inch, absolute 155-3 

Vacuum in condenser, inches of mercury 25.0 

Events of the stroke: 

High-pressure cylinder — " 

Cut-off, crank end 0. 192 

" headend 0.215 

Release, both ends. . 1.00 

Compression, crank end 0.05 

head end 0.05 

Intermediate cylinder — 

Cut-off, both ends. o. 29 

Release, both ends 1. 00 

Compression, crank end 0.03 

" headend 0.04 

Low-pressure cylinder — 

Cut-off, crank end 0.38 

" headend 0.39 

Release, both ends 1.00 

Quality of the steam in the cylinder — (at admission and at compression 
the steam was assumed to be dry and saturated:) 
High-pressure cylinder — 

At cut-off xi 0.785 

At release x 3 o. 899 

Intermediate cylinder — 

At cut-off x t 0.899 

At release X? 0.994 

Low-pressure cylinder — 

At cut-off , xi 0.978 



At release x 2 



super- 
heated 



Interchanges of heat between the steam and the walls of the cylinders, 
in B. T. U. Quantities affected by the positive sign are 
absorbed by the cylinder-walls; quantities affected by the 
negative sign are yielded by the walls. 
High-pressure cylinder — 

Brought in by steam Q 132.92 

During admission Q a 23.54 

During expansion Qb —18.69 

During exhaust Q c — 8.36 



§ 43 1 -] METHODS OF TESTING THE STEAM-ENGINE. 607 

During compression Qa 0.45 

Supplied by jacket Qj 4. 56 

Lost by radiation Q e 1 . 50 

First intermediate receiver — 

Supplied by jacket Qjr 4.92 

Lost by radiation Q e R 0.58 

Intermediate cylinder — 

Brought in by steam Q' 131.89 

During admission Q a ' 13.62 

During expansion Qb — 18.65 

During exhaust Q c ' 0.22 

During compression. . . .'. Qa 0.44 

Supplied by jacket Q/ 6.82 

Lost by radiation Q e ' 2.45 

Second intermediate receiver — 

Supplied by jacket , : . . . .Qjr 4.20 

Lost by radiation Q g R 1 . 20 

Low-pressure cylinder — 

Brought in by steam , Q" 132.14 

During admission Qa' 5.85 

During expansion « Qb" — 9.51 

During exhaust Qc' 2.53 

During compression Qa" 0.00 

Supplied by jacket Q" 7.08 

Lost by radiation c Q" 4. 34 

Total loss by radiation : 

By preliminary test 2Q e 10.07 

By equation (49) 11.68 

Absolute pressures in the cylinder, lbs. per sq. inch : 

High-pressure cylinder — 

Cut-off, crank end 145.9 

" headend *43«2 

Release, crank end 41.3 

" headend , 41.5 

Compression, crank end 43.7 

" headend 48.7 

Admission, crank end 64.5 

" headend 75.3 

Intermediate cylinder — 

Cut-off, crank end , 37.2 

" headend 35.0 

Release, crank end 13.6 

" headend. -3.4 

Compression, crank end 16.3 

head end 17.9 



608 EXPERIMENTAL ENGINEERING. [§43!. 

Admission, crank end 20.4 

" headend 21. 1 

Low-pressure cylinder — 

Cut-off, crank end 12. 1 

" headend 12.0 

Release, crank end 5.6 

" headend 5.4 

Compression and admission, crank end 3.7 

" " " headend 4.3 

Heat equivalents of external work, B. T. U., from areas on indicator- 
diagram to line of absolute vacuum : 
High-pressure cylinder — 

During admission, A W a , crank end 5.71 

" " headend 6.61 

During expansion, A Wb , crank end 10.65 

" " headend 10.81 

During exhaust, A W c , crank end 7.73 

" " headend 8.08 

During compression, A Wd , crank end 0.48 

" " headend 0.62 

Intermediate cylinder — 

During admission, A W a , crank end 7. 58 

" " headend 7.43 

During expansion, A Wb , crank end g. 54 

" " headend g.22 

During exhaust, A W c , crank end 9.27 

" " headend... g.27 

During compression, A Wd , crank end 0.39 

" " headend.... 0.60 

Low-pressure cylinder — 

During admission, A W a , crank end 7.75 

head end 7-99 

During expansion, A IVb, crank end 6.83 

" headend , 6.87 

During exhaust, A W c , crank end 5.08 

" " headend 5.08 

During compression, A Wd , crank end 0.00 

" " headend 0.00 

Power and economy : 

Heat equivalents of work per stroke — 

High-pressure cylinder AW 8.44 

Intermediate cylinder A W' 7. 12 

Low-pressure cylinder AW" 9.64 

Total 25.20 

Total heat furnished by jackets 27.58 



§43 I -J METHODS OF TESTING THE STEAM-ENGINE. 609 

Distribution of work : 

High-pressure cylinder 1.00 

Intermediate cylinder o. 84 

Low-pressure cylinder 1. 14 

Horse-power 104.9 

Steam per horse-power per hour 14-65 

B. T. U. per horse-power per minute 258.3 

The Saturation-curve. — By drawing on the indicator- 
diagram a curve corresponding to the volume of an equal 
weight of dry and saturated steam, the quality may be 
determined at any point during the expansion, and by calcula- 
tions similar to those used in Hirn's analysis the heat exist- 
ing in the cylinder may be computed. The method of 
drawing the saturation-curve may be explained as follows: 
first, determine the weight of steam per stroke by the usual 
methods of engine-testing. Second, find the corresponding 
volume for dry and saturated steam by multiplying the weight 
of steam per stroke by the volume corresponding to one 
pound as obtained from the steam tables, for several points in 
the expansion-curve. Third, draw in connection with the 
indicator-diagram a clearance-line and a vacuum-line in 
accordance with the scale of volume and pressure, from which 
initial measurements can be taken. 

Fourth, determine the volume occupied by the steam 
caught in the clearance-space when compressed to the steam- 
line; for this operation we can assume with little error that 
the steam is dry and saturated at the end of compression, and 
that it remains in this condition during compression. Thus 
in Fig. 283 the compression-line is produced from a b to a 
by drawing a saturation-curve, which is drawn by taking 
ordinates proportional to pressures and abscissa proportional 
to volumes as given in the steam table, those for a b being 
known. This curve may be considered the curve of volume 
for dry and saturated compression. Very little error would 
be made by assuming the compression-curve hyperbolic. By 
producing the saturation-curve aa b downward the quality 
during compression could be determined. 



6io 



EXPERIMEN TA L ENGINEERING. 



[§43I- 



Fifth, lay off from the compression-curve for saturated 
steam horizontal distance corresponding to the volume of dry 
and saturated steam at different pressures, obtained as ex- 
plained above. Through the various points so determined 
draw a curve; such a curve will be the saturation-curve. 

To obtain the quality of the steam at any point on the 
expansion-lines divide the horizontal distance measured from 
the clearance-line to the expansion-line by the corresponding 
distance to the saturation-curve. Thus in Fig. 283 the 




Fig. 283. 



quality at d t is equal to b x djb x c x — that is, the quality is the 
ratio of the actual volume of the steam to that of dry and 
saturated steam, and this is true provided the volume occupied 
by the condensed steam, which is exceedingly small in every 
case, is neglected. The quality at different points during 
expansion can be determined in a similar manner, and a curve 
showing the variation of quality may be laid off as shown in 
the lower portion of Fig. 283. 

The comparative quality during compression can be 
obtained in a similar manner by comparing the volume during 
compression with that of an equal volume of d:y and saturated 
steam. 



§43*0 METHODS OF TESTING THE STEAM-ENGINE, 6ll 

The error involved in the above construction is the same 
as that made in Hirn's analysis, since in both cases the 
quality of the steam at end of compression is assumed and the 



80- 



?0 



V 




Fig. 284. 

volume of water entrained is neglected ; such errors are, how- 
ever, exceedingly small. Fig. 284 shows the saturation- 
curves of a combined diagram reduced from cards taken on 
the Sibley College experimental engine. It will be noticed 
that the saturation-curve is not continuous for the three 



612 



EXPERIMENTAL ENGINEERING. 



[§43L 



cylinders, which is due to the fact that clearance and com- 
pression of the different cylinders is not uniform. 

To calculate the interchanges of heat in an engine during 
expansion and compression, first determine the quality as 
explained. Also determine the weight of steam used per 
stroke, the weight of and the rise in temperature of the con- 
densing water. Using the same symbols as for Hirn's 
analysis, the heat supplied to the engine will be 

Q=M(xr + q); 

that discharged from the engine is equal to the heat of the 
condensed steam above 32 ° F., Mq s plus that absorbed by the 
injection-water G(q k — q) that utilized in work A W. The 



HEAT-INTERCHANGES CALCULATED BY SATURATION-CURVE. 

QUANTITY PER IOO STROKES. 



Obtain by measurement : 

Weight of steam, in pounds 
Weight of injection water, 


M 
G 

<ls 

qk - qi 
M 

X 

X\ , x* 1 and x% 

IOO 

H 
Hi 
H, 
H % 
Mq g =K 
M(qk — qi) = R~i 


Heat transformed into work ; 
Admission (a) A W a = a 

Expansion (b) A Wb = b 

Exhaust (c) AJV c = c 

Compression (d) A Wd = d 

Heat-interchanges : 
Admission H — {Hi -f- a) 

Expansion H x — {H % -\- b) 


Temperature of condensed 
steam above 32 F 

Rise in temperature injec- 
tion-water 

Wt. of steam in clearance . . 

Quality steam entering 

Quality cut-off, release, and 


Quality end of compres'n, % 
Obtain by computation .* 

Total heat M(xr -f q) 

Heat at cut-off, 

(M+M )(xiPi+?i) 
Heat at release, 

Heat at compression, 

M*{x % p*-\-qz) 
Heat discharged, condensed 


Exhaust H a - (HT-\- K, + c + H t ) 
Compression H 9 — (d-\- H t ) 

Total loss equals algebraic sum 
of heat-interchanges, and this 
affords a check on the numer- 
ical work. 


Heat discharged, injection 













§431-] METHODS OF TESTING THE STEAM-ENGINE. 613 

difference between that received and that discharged is the 
total loss due to radiation. 

The heat remaining in the steam at any point can be 
obtained by multiplying the weight of steam used per stroke, 
increased by that caught in the clearance, by the sum of 
sensible heat and product of internal latent heat and quality. 
Thus 

H=(M+M,)(g + xp). 

The work done while the piston is passing from point to point 
under consideration may be obtained by integrating the 
diagram and reducing to heat-units by dividing by 778. The 
table on the foregoing page indicates the operations to be 
performed in calculating the heat-interchanges by the satura- 
tion-curve. 

Note. — The method of determining the heat interchanges in a steam 
engine which have been given apply directly to the use of saturated or 
wet steam only. The same general method is applicable when super- 
heated steam is used, but for that case the relation of volume and weights 
to heat values will be essentially different. 



CHAPTER XIX. 

METHODS OF TESTING PUMPING ENGINES AND 
STEAM LOCOMOTIVES. 

432. Special Methods of Engine-testing.— Engines em< 

ployed for certain specific purposes, as for pumping water or 
for locomotive service, are constructed with peculiar features 
rendered necessary by the work to be accomplished. In such 
cases it is frequently difficult to arrange to make all the 
measurements in the manner prescribed for the tests of the 
general type of the steam-engine ; further, it is often of impor- 
tance that the amount and character of the work accomplished 
be taken into consideration. To secure results that can safely 
be compared, it is essential that certain methods of testing be 
adopted and that the results be expressed in the same form 
and referred to the same standards. 

433. Method of Testing Steam Pumping-engines. — A 
standard method of testing steam pumping-engines has been 
adopted by the American Society of Mechanical Engineers 
(see Vol. XL of the Transactions). The method is as follows : 

(i) TEST OF FEED-WATER TEMPERATURES. 

The plant is subjected to a preliminary run, under the con- 
ditions determined upon for the test, for a period of three 
hours, or such a time as is necessary to find the temperature 
of the feed-water (or the several temperatures, if there is more 
than one supply) for use in the calculation of the duty. During 
this test observations of the temperature are made every fifteen 
minutes. Frequent observations are also made of the speed, 
length of stroke, indication of water-pressure gauges, and other 

614 



§ 43 2 -] TESTING PUMPING-ENGINES. 6 1 5, 

instruments, so as to have a record of the general conditions 
under which this test is made. 

Directions for obtaining Feed-water Temperatures. — When 
the feed-water is all supplied by one feeding instrument, the 
temperature to be found is that of the water in the feed-pipe 
near the point where it enters the boiler. If the water is fed 
by an injector this temperature is to be corrected for the heat 
added to the water by the steam, and for this purpose the 
temperature of the water entering and of that leaving the 
injector are both observed. If the water does not pass through 
a heater on its way to the boiler (that is, that form of heater 
which depends upon the rejected heat of the engine, such as 
that contained in the exhaust-steam either of the main cylin- 
ders or of the auxiliary pumps), it is sufficient, for practical 
purposes, to take the temperature of the water at the source 
of supply, whether the feeding instrument is a pump or an 
injector. 

When there are two independent sources of feed-water 
supply, one the main supply from the hot-well, or from some 
other source, and the other an auxiliary supply derived from 
the water condensed in the jackets of the main engine and in 
the live-steam reheater, if one be used, they are to be treated 
independently. The remarks already made apply to the first, 
or main, supply. The temperature of the auxiliary supply, if 
carried by an independent pipe either direct to the boiler or to 
the main feed-pipe near the boiler, is to be taken at convenient 
points in the independent pipe. 

When a separator is used in the main steam-pipe, arranged 
so as to discharge the entrained water back into the boiler by 
gravity, no account need be made of the temperature of the 
water thus returned. Should it discharge either into the 
atmosphere to waste, to the hot-well, or to the jacket-tank, its 
temperature is to be determined at the point where the water 
leaves the separator before its pressure is reduced. 

When a separator is used, and it drains by gravity into the 
jacket-tank, this tank being subjected to boiler-pressure, the 



6i6 



EXPERIMENTAL ENGINEERING. 



[§ 432. 



temperature of the separator-water and jacket-water are each 
to be taken before their entrance to the tank. 

Should there be any other independent supply of water, the 
temperature of that is also to be taken on this preliminary test. 

Directions for Measurement of Feed-water. — As soon as the 
feed-water temperatures have been obtained the engine is 
stopped, and the necessary apparatus arranged for determin- 
ing the weight of the feed-water consumed, or of the various 
supplies of feed-water if there is more than one. 

In order that the main supply of feed-water may be meas- 
ured, it will generally be found desirable to draw it from the 
cold-water service-main. The best form of apparatus for 
weighing the water consists of two tanks, one of which rests 
upon a platform-scale supported by staging, while the other is 
placed underneath. The water is drawn from the service-main 
into the upper tank, where it is weighed, and it is then emptied 
into the lower tank. The lower tank serves as a reservoir, and 
to this the suction-pipe of the feeding apparatus is connected. 

The jacket-water may be measured by using a pair of small 
barrels, one being filled while the other is being weighed and 
emptied. This water, after being measured, may be thrown 
away, the loss being made up by the main feed-pump. To 
prevent evaporation from the water, and consequent loss on 
account of its highly heated condition, each barrel should be 
partially filled with cold water previous to using it for collect- 
ing the jacket-water, and the weight of this water treated as 
tare. 

When the jacket-water drains back by gravity to the boiler, 
waste of live steam during the weighing should be prevented 
by providing a small vertical chamber, and conducting the 
water into this receptacle before its escape. A glass water- 
gauge is attached, so as to show the height of water inside the 
chamber, and this serves as a guide in regulating the discharge- 
valve. 

When the jacket-water is returned to the boiler by means 
of a pump, the discharge-valve should be throttled during the 
test, so that the pump may work against its usual pressure, 



§ 43 2 °] TESTING PUMPING-ENGINES. 617 

that is, the boiler-pressure as nearly as may be, a gauge being 
attached to the discharge-pipe for this purpose. 

When a separator is used and the entrained water dis- 
charges either to waste, to the hot-well, or to the jacket-tank, 
the weight of this water is to be determined, the water being 
drawn into barrels in the manner pointed out for measuring 
the jacket-water. Except -in the case where the separator dis- 
charges into the jacket-tank, the entrained water thus found is 
treated, in the calculations, in the same manner as moisture 
shown by the calorimeter-test. When it discharges into the 
jacket-tank, its weight is simply subtracted from the total 
weight of water fed, and allowance made for heat of this water 
lost by radiation between separator and tank. 

When the jackets are drained by a trap, and the condensed 
water goes either to waste or to the hot-well, the determination 
of the quantity used is not necessary to the main object of the 
duty trial, because the main feed-pump in such cases supplies 
all the feed-water. For the sake of having complete data, how- 
ever, it is desirable that this water be measured, whatever the 
use to which it is applied. 

Should live steam be used for reheating the steam in the 
intermediate receiver, it is desirable to separate this from the 
jacket-steam, if it drain into the same tank, and measure it 
independently. This, likewise, is not essential to the main 
object of the duty trial, though useful for purposes of in- 
formation. 

The remarks as to the manner of preventing losses of live 
steam and of evaporation, in the measurement of jacket-water, 
apply to the measurement of any other hot water under press- 
ure, which may be used for feed-water. 

Should there be any other independent supply of water to 
the boiler, besides those named, its quantity is to be deter- 
mined independently, apparatus for all these measurements 
being set up during the interval between the preliminary ru» 
and the main trial, when the plant is idle. 



6l8 EXPERIMENTAL ENGINEERING. [§432. 

(2) THE MAIN DUTY-TRIAL. 

The duty-trial is here assumed to apply to a complete 
plant, embracing a test of the performance of the boiler as 
well as that of the engine. The test of the two will go on 
simultaneously after both are started, but the boiler-test will 
begin a short time in advance of the commencement of the 
engine-test, and continue a short time after the engine-test is 
finished. The mode of procedure is as follows : 

The plant having been worked for a suitable time under 
normal conditions, the fire is burned down to a low point and 
the engine brought to rest. The fire remaining on the grate is 
then quickly hauled, the furnace cleaned, and the refuse with- 
drawn from the ash-pit. The boiler-test is now started, and 
this test is made in accordance with the rules for a standard 
method recommended by the Committee on Boiler Tests of 
the American Society of Mechanical Engineers. This method, 
briefly described, consists in starting the test with a new fire 
lighted with wood, the boiler having previously been heated to 
its normal working degree ; operating the boiler in accordance 
with the conditions determined upon ; weighing coal, ashes, 
and feed-water ; observing the draught, temperatures of feed- 
water and escaping gases, and such other data as may be inci- 
dentally desired ; determining the quantity of moisture in the 
coal and in the steam ; and at the close of the test hauling the 
fire, and deducting from the weight of coal fifed whatever 
unburned coal is contained in the refuse withdrawn from the 
furnace, the quantity of water in the boiler and the steam-press- 
ure being the same as at the time of lighting the fire at the 
beginning of the test. 

Previous to the close of the test it is desirable that the fire 
should be burned down to a low point, so that the unburned 
coal withdrawn may be in a nearly consumed state. The tem- 
perature of the feed-water is observed at the point where the 
water leaves the engine heater, if this be used, or at the point 
where it enters the flue-heater, if that apparatus be employed. 
Where an injector is used for supplying the water, a deduction 



§ 43 2 J TES TING P UMPING-ENGINES. 6 1 9 

is to be made in either case for the increased temperature of 
the water derived from the steam which it consumes. 

As soon after the beginning of the boiler-test as practicable 
the engine is started and preparations are made for the begin- 
ning of the engine-test. The formal commencement of this 
test is delayed till the plant is again in normal working con- 
dition, which should not be over one hour after the time of 
lighting the fire. When the time for commencement arrives 
the feed-water is momentarily shut off, and the water in the 
lower tank is brought to a mark. Observations are then made 
of the number of tanks of water thus far supplied, the height 
of water in the gauge-glass of the boiler, the indication of the 
counter on the engine, and the time of day ; after which the 
supply of feed-water is renewed, and the regular observations 
of the test, including the measurement of the auxiliary supplies 
of feed-water, are commenced. The engine-test is to continue 
at least ten hours. At its expiration the feed-pump is again 
momentarily stopped, care having been taken to have the 
water slightly higher than at the start, and the water in the 
lower tank is brought to the mark. When the water in the 
gauge-glass has settled to the point which it occupied at the 
beginning, the time of day and the indication of the counter 
are observed, together with the number of tanks of water thus 
far supplied, and the engine-test is held to be finished. The 
engine continues to run after this time till the fire reaches a 
condition for hauling, and completing the boiler-test. It is 
then stopped, and the final observations relating to the boiler- 
test are taken. 

The observations to be made and data obtained for the 
purposes of the engine-test, or duty-trial proper, embrace the 
weight of feed-water supplied by the main feeding apparatus, 
that of the water drained from the jackets, and any other water 
which is ordinarily supplied to the boiler, determined in the 
manner pointed out. They also embrace the number of hours' 
duration, and number of single strokes of the pump during the 
test ; and, in direct-acting engines, the length of the stroke, 
together with the indications of the gauges attached to the 






620 EXPERIMENTAL ENGINEERING. [§ 43 2 - 

force and suction mains, and indicator-diagrams from the steam- 
cylinders. It is desirable that pump-diagrams also be obtained. 

Observations of the length of stroke, in the case of direct- 
acting engines, should be made every five minutes; observa- 
tions of the water-pressure gauges every fifteen minutes ; 
observations of the remaining instruments — such as steam- 
gauge, vacuum-gauge, thermometer in pump-well, thermome- 
ter in feed-pipe; thermometer showing temperature of engine- 
room, boiler-room, and outside air; thermometer in flue, ther- 
mometer in steam-pipe, if the boiler has steam-heating surface, 
barometer, and other instruments which may be used — every 
half-hour. Indicator-diagrams should be taken every half-hour. 

When the duty-trial embraces simply a test of the engine, 
apart from the boiler, the course of procedure will be the same 
as that described, excepting that the fires will not be hauled, 
and the special observations relating to the performance of the 
boiler will not be taken. 

Directions regarding Arrangement and Use of Instruments, 
and other Provisions for the Test. — The gauge attached to the 
force-main is liable to a considerable amount of fluctuation 
unless the gauge-cock is nearly closed. The practice of 
choking the cock is objectionable. The difficulty may be 
satisfactorily overcome, and a nearly steady indication se- 
cured, with cock wide open, if a small reservoir having an air- 
chamber is interposed between the gauge and the force-main. 
By means of a gauge glass on the side of the chamber and an 
air-valve, the average water-level may be adjusted to the 
height of the centre of the gauge, and correction for this 
element of variation is avoided. If not thus adjusted, the 
reading is to be referred to the level shown, whatever this 
may be. 

To determine the length of stroke in the case of direct act- 
ing engines, a scale should be securely fastened to the frame 
which connects the steam and water cylinders, in a position 
parallel to the piston-rod, and a pointer attached to the rod so 
as to move back and forth over the graduations on the scale. 
The marks on the scale, which the pointer reaches at the two 



§ 43 2 -] TESTING PUMPING-ENGINES. 62 I 

ends of the stroke, are thus readily observed, and the distance 
moved over computed. If the length of the stroke can be de- 
termined by the use of some form of registering apparatus, 
such a method of measurement is preferred. The personal 
errors in observing the exact scale-marks, which are liable to 
creep in, may thereby be avoided. 

The form of calorimeter to be used for testing the quality 
of the steam is left to the decision of the person who conducts 
the trial. It is preferred that some form of continuous calo- 
rimeter be used, which acts directly on the moisture tested. If 
either the separating calorimeter* or the wire-drawing f 
instrument be employed, the steam which it discharges is to be 
measured either by numerous short trials, made by condensing 
it in a barrel of water previously weighed, thereby obtaining the 
rate by which it is discharged, or by passing it through a sur- 
face-condenser of some simple construction, and measuring the 
whole quantity consumed. When neither of these instruments 
is at hand, and dependence must be placed upon the barrel 
calorimeter, scales should be used which are sensitive to a 
change in weight of a small fraction of a pound, and thermom- 
eters which may be read to tenths of a degree. The pipe 
which supplies the calorimeter should be thoroughly warmed 
and drained just previous to each test. In making the calcu- 
lations the specific heat of the material of the barrel or tank 
should be taken into account, whether this be of metal or of 
wood. 

If the steam is superheated, or if the boiler is provided 
with steam-heating surface, the temperature of the steam is to 
be taken by means of a high-grade thermometer resting in a 
cup holding oil or mercury, which is screwed into the steam- 
pipe so as to be surrounded by the current of steam. The 
temperature of the feed-water is preferably taken by means of 
a cup screwed into the feed-pipe in the same manner. 

Indicator-pipes and connections used for the water-cylin- 

* Vol. vii, p. 178, 1886, Transactions A. S. M. E. See page 430 of this 
volume. 

f Vol. XI, 1890, p. 193, Transactions A. S. M. E. See page 419 of this volume, 



622 EXPERIMENTAL ENGINEERING. [§ 432. 

ders should be of ample size, and, so far as possible, free from 
bends. Three-quarter-inch pipes are preferred, and the indi- 
cators should be attached one at each end of the cylinder. It 
should be remembered that indicator-springs which are correct 
under steam heat are erroneous when used for cold water. When 
such springs are used, the actual scale should be determined, 
if calculations are made of the indicated work done in the 
water-cylinders. The scale of steam-springs should be deter- 
mined by a comparison, under steam-pressure, with an accurate 
steam-gauge at the time of the trial, and that of water-springs 
by cold dead-weight test. 

The accuracy of all the gauges should be carefully verified 
by comparison with a reliable mercury-column. Similar veri- 
fication should be made of the thermometers, and if no stand- 
ard is at hand, they should be tested in boiling water and 
melting ice. 

To avoid errors in conducting the test, due to leakage of 
stop-valves either on the steam-pipes, feed-water pipes, or 
blow-off pipes, all these pipes not concerned in the operation 
of the plant under test should be disconnected. 

(3) LEAKAGE-TEST OF PUMP. 

As soon as practicable after the completion of the main 
trial (or at some time immediately preceding the trial) the en- 
gine is brought to rest, and the rate determined at which leak- 
age takes place through the plunger and valves of the pump, 
when these are subjected to the full pressure of the force- 
main. 

The leakage of the plunger is most satisfactorily determined 
by making the test with the cylinder-head removed. A wide 
board or plank may be temporarily bolted to the lower part of 
the end of the cylinder, so as to hold back the water in the 
manner of a dam, and an opening made in the temporary head 
thus provided for the reception of an overflow pipe. The 
plunger is blocked at some intermediate point in the stroke (or, 
if this position is not practicable, at the end of the stroke), and 



§ 43 2 • ] TESTING P UMPING- ENGINES. 623 

the water from the force-main is admitted at full pressure be. 
hind it. The leakage escapes through the overflow pipe, and 
it is collected in barrels and measured. 

Should the escape of the water into the engine-room be 
objectionable, a spout may be constructed to carry it out of the 
building. Where the leakage is too great to be readily meas- 
ured in barrels, or where other objections arise, resort may be 
had to weir or orifice measurement, the weir or orifice taking 
the place of the overflow-pipe in the wooden head. The ap- 
paratus may be constructed, if desired, in a somewhat rude 
manner, and yet be sufficiently accurate for practical require- 
ments. The test should be made, if possible, with the plunger 
in various positions. 

In the case of a pump so planned that it is difficult to re- 
move the cylinder-head, it may be desirable to take the leakage 
from one of the openings which are provided for the inspection 
of the suction-valves, the head being allowed to remain in 
place. 

It is here assumed that there is a practical absence of valve- 
leakage, a condition of things which ought to be attained in all 
well-constructed pumps. Examination for such leakage should 
be made first of all, and if it occurs and it is found to be due 
to disordered valves, it should be remedied before making the 
plunger-test. Leakage of the discharge-valves will be shown 
by water passing down into the empty cylinder at either end 
when they are under pressure. Leakage of the suction-valves 
will be shown by the disappearance of water which covers 
them. 

If valve-leakage is found which cannot be remedied, the 
quantity of water thus lost should also be tested. The deter- 
mination of the quantity which leaks through the suction-valves, 
where there is no gate in the suction-pipe, must be made by 
indirect means. One method is to measure the amount of 
water required to maintain a certain pressure in the pump- 
cylinder when this is introduced through a pipe temporarily 
erected, no water being allowed to enter through the discharge* 
valves of the pump. 



624 



EXPERIMENTAL ENGINEERING. 



[§ 43* 



The exact methods to be followed in any particular case, in 
determining leakage, must be left to the judgment and ingenu- 
ity of the person conducting the test. 

(4) TABLE OF DATA AND RESULTS. 

In order that uniformity may be secured, it is suggested 
that the data and results, worked out in accordance with the 
standard method, be tabulated in the manner indicated in the 
following scheme : 

Duty-trial of Engine. 
Dimensions. 

1. Number of steam-cylinders 

2. Diameter of steam-cylinders ins. 

3. Diameter of piston-rods of steam-cylinders ins. 

4. Nominal stroke of steam-pistons ft. 

5. Number of water-plungers. 

6. Diameter of plungers ins. 

7. Diameter of piston-rods of water-cylinders ins. 

8. Nominal stroke of plungers ft. 

9. Net area of plungers sq. ins. 

10. Net area of steam-pistons sq. ins. 

11. Average length of stroke of steam-pistons during trial ft. 

12. Average length of stroke of plungers during trial ft. 

(Give also complete description of plant.) 

Temperatures. 

13. Temperature of water in pump- well degs. 

14. Temperature of water supplied to boiler by main feed-pump. degs. 

15. Temperature of water supplied to boiler from various other 

sources degs. 

Feed-water. 

16. Weight of water supplied to boiler by main feed-pump lbs. 

17. Weight of water supplied to boiler from various other sources, lbs. 

18. Total weight of feed-water supplied from all sources. - lbs. 

Pressures. 

19. Boiler-pressure indicated by gauge lbs. 

20. Pressure indicated by gauge on force-main lbs. 

21. Vacuum indicated by gauge on suction-main ins. 

22. Pressure corresponding to vacuum given in preceding line lbs. 

23. Vertical distance between the centres of the two gauges ins. 

24. Pressure equivalent to distance between the two gauges lbs. 



§ 43 2 -] TESTING PUM PING-ENGINES, 625 

Miscellaneous Data. 

25. Duration of trial hrs. 

26. Total number of single strokes during trial 

27. Percentage of moisture in steam supplied to engine, or num- 

ber of degrees of superheating . . . o % or deg. 

28. Total leakage of pump during trial, determined from results of 

leakage-test lbs. 

29. Mean effective pressure, measured from diagrams taken from 

steam-cylinders M.E.P. 

Principal Results. 

30. Duty ". ft.-lbs. 

31. Percentage of leakage % 

32. Capacity gals. 

33. Percentage of total frictions. % 

Additional Results* 

34. Number of double strokes of steam-piston per minute 

35. Indicated horse-power developed by the various steam- 

cylinders I. H. P. 

36. Feed-water consumed by the plant per hour lbs. 

' 37. Feed-water consumed by the plant per indicated horse-power 

per hour, corrected for moisture in steam lbs. 

38. Number of heat-units consumed per indicated horse-power per 

hour B. T.U. 

39. Number of heat-units consumed per indicated horse-power per 

minute • B. T.U. 

40. Steam accounted for by indicator at cut-off and release in the 

various steam-cylinders lbs. 

41. Proportion which steam accounted for by indicator bears to 

the feed-water consumption 

Sample Diagrams taken from Steam-cylinders. 

[Also, if possible, full measurements of the diagrams, embracing pressures 
at the initial point, cut-off, release, and compression ; also back-pressure, and 
the proportions of the stroke completed at the various points noted.] 

42. Number of double strokes of pump per minute 

43. Mean effective pressure, measured from pump-diagrams M. E.P. 

44. Indicated horse-power exerted in pump-cylinders I. H. P. 

■ » , . , 

* These are not necessary to the main object, but it is desirable to give them, 



626 EXPERIMENTAL ENGINEERING. [§432. 

Sample Diagrams taken from Pump-cylinders. 



Data and Results of Boiler-test. 

[in accordance with the scheme recommended by the boiler-test 
committee of the society.] 

1. Date of trial 

2. Duration of trial . hrs. 

Dimensions and Proportions. 

3. Grate-surface wide long Area sq.ft. 

4. Water-heating surface sq. ft. 

5. Superheating-surface sq. ft. 

6. Ratio of water-heating surface to grate-surface 

(Give also complete description of boilers.) 

Average Pressures. 

7. Steam-pressure in boiler by gauge lbs. 

• 8. Atmospheric pressure by barometer , lbs. 

9. Force of draught in inches of water ins. 

Average Temperatures. 

10. Of steam degs. 

11. Of escaping gases degs. 

12. Of feed-water. . .... 

Fuel. 

13. Total amount of coal consumed * lbs, 

14. Moisture in coal % 

15. Dry coal consumed lbs. 

16. Total refuse (dry) lbs. 

17. Total combustible (dry weight of coal, item 15, less refuse, 

item 16) lbs. 

18. Dry coal consumed per hour lbs. 

Results of Calorifnetric Test. 

19. Quality of steam, dry steam being taken as unity 

20. Percentage of moisture in steam % 

.21, Number of degrees superheated degs. 

* Including equivalent of wood used in lighting fire. One pound of wood 
equals 0.4 of a pound of coal, not including unburned coal withdrawn from fire 
at end of test. 



§ 43 2 -] TESTING PUMPING-ENGINES. 627 

Water. 

22. Total weight of water pumped into boiler and apparently 

evaporated * lbs. 

23. Water actually evaporated corrected for quality of steam lbs. 

24. Equivalent water evaporated into dry steam from and at 

212 F.f lbs. 

25. Equivalent total heat derived from fuel, in British thermal 

units B.T.U. 

26. Equivalent water evaporated into dry steam from and at 

212° F. per hour \. lbs. 

Economic Evaporation. 

27. Water actually evaporated per pound of dry coal from actual 

pressure and temperature lbs. 

28. Equivalent water evaporated per pound of dry coal from 

and at 212 F lbs. 

29. Equivalent water evaporated per pound of combustible from 

and at 212 F lbs. 

30. Number of pounds of coal required to supply one million 

British thermal units lbs. 

Rate of Combustion. 

31. Dry coal actually burned per square foot of grate-surface per 
hour lbs. 

Rate of Evaporation. 

• 32. Water evaporated from and at 212 F. per square foot of 

heating-surface per hour • lbs. 

To determine the percentage of surface moisture in the coal 
a sample of the coal should be dried for a period of twenty- 
four hours, being subjected to a temperature of not more than 
212 . The quantity of unconsumed coal contained in the 
refuse withdrawn from the furnace and ash-pit at the end of the 
test may be found by sifting either the whole of the refuse, or 



* Corrected for inequality of water-level and of steam-pressure at beginning 
and end of test. 

TT I 

f Factor of evaporation = — , H and h being, respectively, the total 

heat-units in steam of the average observed pressure corrected for quality, 
and in water of the average observed temperature of feed, 



628 



EXPERIMENTAL ENGINEERING. 



[§432. 



a sample of the same, in a screen having f-inch meshes. This, 
deducted from the weight of dry coal fired, gives the weight 
of dry coal consumed, for line 15. 

Results of actual trial, as illustrated by the committee, 
would be computed by the use of the following formulae : 

Foot-pounds of work done 
I. Duty = Tota i num ber of heat-units consumed X I ' 000 >° 00 

A{P±p + s)xLxN 
= -jT X 1, 000,000 (foot-pounds). 



C X 144 
2. Percentage of leakage = . j tj. X 100 (per cent). 



3. Capacity = number of gallons of water discharged in 24 
hours 

_ A x Lx Nx 7.4805 X 24 
~DX 144 



A XLx NX 1.2467s 
D 



(gallons). 



4. Percentage of total friction 



( IHp _ A{P±p+s)xLxN \ 
_ ( J _ ^J D X 60 X 33>QQQ ) 



LH.P. 



x 100 



r A{P±pXs)x Lx N~] , . 

= 1 1 - A s xM.E.P.xL s xN; 1 X ^o (per cent); 

or, in the usual case, where the length of the stroke and num- 
ber of strokes of the plunger are the same as that of the steam- 
piston, this last formula becomes — 

r A(P±p+s)~\ , x 

Percentage of total frictions = I — • . ^ n/r p p ]X iOO(p.c). 



§ 43 2 -] TESTING PUMPING-ENGINES. 629 

In these formulae the letters refer to the following quanti- 
ties : 

A — Area, in square inches, of pump-plunger or piston, 
corrected for area of piston-rod. (When one rod 
is used at one end only, the correction is one half 
the area of the rod. If there is more than one 
rod, the correction is multiplied accordingly.) 

P= Pressure, in pounds per square inch, indicated by 
the gauge on the force-main. 

p = Pressure, in pounds per square inch, corresponding 
to indication of the vacuum-gauge on suction- 
main (or pressure-gauge, if the suction-pipe is 
under a head). The indication of the vacuum- 
gauge, in inches of mercury, may be converted 
into pounds by dividing it by 2.035. 

S = Pressure, in pounds per square inch, corresponding 
to distance between the centres of the two gauges. 
The computation for this pressure is made by 
multiplying the distance, expressed in feet, by the 
weight of one cubic foot of water at the tempera- 
ture of the pump-well, and dividing the product 
by 144 ; or by multiplying the distance in feet by 
the weights of one cubic foot of water at the 
various temperatures. 

£, = Average length of stroke of pump-plunger, in feet. 

N= Total number of single strokes of pump-plunger 

made during the trial. 
A = Area of steam-cylinder, in square inches, corrected 
for area of piston-rod. The quantity A s xM.£.P. f 
in an engine having more than one cylinder, is 
the sum of the various quantities relating to the 
respective cylinders. 

L s = Average length of stroke of steam-piston, in feet. 

N s = Total number of single strokes of steam-piston 
during trial. 
M.E.P. = Average mean effective pressure, in pounds per 



63O EXPERIMENTAL ENGINEERING. [§ 432. 

square inch, measured from the indicator-diagrams 
taken from the steam cylinder. 
I.H.P. = Indicated horse-power developed by the steam- 
cylinder. 
C — Total number of cubic feet of water which leaked 
by the pump-plunger during the trial, estimated 
from the results of the leakage-test. 
D = Duration of trial, in hours. 

H = Total number of heat-units [B. T. U.] consumed by 
engine = weight of water supplied to boiler by 
main feed-pump X. total heat of steam of boiler- 
pressure reckoned from temperature of main feed- 
water -f- weight of water supplied by jacket-pump 
X total heat of steam of boiler-pressure reckoned 
from temperature of jacket-water -|- weight of any 
other water supplied X total heat of steam reck- 
oned from its temperature of supply. The total 
heat of the steam is corrected for the moisture or 
superheat which the steam may contain. For 
moisture, the correction is subtracted, and is found 
by multiplying the latent heat of the steam by the 
percentage of moisture, and dividing the product 
by 100. For superheat, the correction is added, 
and is found by multiplying the number of 
degrees of superheating (i.e., the excess of the 
temperature of the steam above the normal tem- 
perature of saturated steam) by 0.48. No allow- 
ance is made for heat added to the feed-water, 
which is derived from any source, except the 
engine or some accessory of the engine. Heat 
added to the water by the use of a flue-heater at 
the boiler is not to be deducted. Should heat be 
abstracted from .the flue by means of a steam- 
reheater connected with the intermediate receiver 
of the engine, this heat must be included in the 
total quantity supplied by the boiler. 
The following example is one of those given by the com- 



432.] TESTING PUMPING-ENGINES. 63 I 

mittee to illustrate the method of computation. The figures 
are not obtained from tests actually made, but they correspond 
in round numbers with those which were so obtained: 

EXAMPLE. — Compound Fly-wJieel Engine. — High -pressure 
cylinder jacketed with live steam from the boiler. Low-press- 
ure cylinder jacketed with steam from the intermediate re- 
ceiver, the condensed water from which is returned to the 
boiler by means of a pump operated by the engine. Main 
steam-pipe fitted with a separator. The intermediate receiver 
provided with a reheater supplied with boiler-steam. Water 
drained from high-pressure jacket, separator, and reheater col- 
lected in a closed tank under boiler-pressure, and from this 
point fed to the boiler direct by an independent steam-pump. 
Jet-condenser used operated by an independent air-pump. 
Main supply of feed-water drawn from hot-well and fed to the 
boiler by donkey steam-pump, which discharges through a 
feed-water heater. All the steam-pumps, together with the 
independent air-pump, exhaust through the heater to the at- 
mosphere. 

DIMENSIONS. 

Diameter of high-pressure steam-cylinder (one) 20 in. 

Diameter of low-pressure steam-cylinder (one) 40 " 

Diameter of plunger (one) 20 " 

Diameter of each piston-rod 4. " 

Stroke of steam-pistons and pump-plunger 3 ft. 

GENERAL DATA. 

1. Duration of trial (Z>) 10 hrs. 

2. Boiler-pressure indicated by gauge (barometric press- 

ure, 14. 7 lbs. ) 120 lbs. 

3. Temperature of water in pump-well 60 degs 

4. Temperature of water supplied to boiler by main feed- 

pump, leaving heater 215 

5. Temperature of water supplied by low-pressure jacket- 

pump 225 

6. Temperature of water supplied by high-pressure 

jacket, separator, and reheater-pump, that derived 
from separator being 340 , and that from jackets 
200 .. 300 " 



632 EXPERIMENTAL ENGINEERING. [§ 432. 

7. Weight of water supplied to boiler by main feed-pump 18,863 lbs. 

8. Weight of water supplied by low-pressure jacket-pump 615 " 

9. Weight of water supplied by pump for high-pressure 

jacket, separator, and reheater-tank, of which 210 

lbs. is derived from separator 1 ,025 " 

10. Total weight of feed- water supplied from all sources 20,503 " 

11. Percentage of moisture in steam after leaving sepa- 

rator 1.5$ 

DATA RELATING TO WORK OF PUMP. 

12. Area of plunger minus \ area of piston-rod (A) 307.88 sq. in. 

13. Average length of stroke (L and L s ) 3 ft. 

14. Total number of single strokes during trial (N and N s ) 24,000 

15. Pressure by gauge on force-main (P) 95 lbs. 

16. Vacuum by gauge.on suction-main 7.5 in. 

17. Pressure corresponding to vacuum given in preceding 

line (/) 3.69 lbs. 

18. Vertical distance between centres of two gauges 10 ft. 

19. Pressure equivalent to distance between two gauges (s) 4.33 lbs c 

20. Total leakage of pump during trial, determined from 

results of leakage-test (C) 3,078 cu. ft. 

21. Number of double strokes of pump per minute 20 

22. Mean effective pressure measured from pump-dia- 

grams 105 lbs. 

23. Indicated horse-power exerted in pump-cylinders.. .. H7-55 I.H.P. 



DATA RELATING TO WORK OF STEAM-CYLINDERS. 

24. Area of high-pressure piston minus -£■ area of rod (A S i) 307.88 sq. in. 

25. Area of low-pressure piston minus i area of rod (A s2 ) 1,250.36 " " 

26. Average length of stroke, each 3 ft. 

27. Mean effective pressure measured from high-pressure 

diagrams {M.E.P.i) 59-25 lbs. 

28. Mean effective pressure measured from low-pressure 

diagrams (M.E.P. 2 ) 13-60 " 

29. Number of double strokes per minute (line 21) 20 

30. Indicated horse-power developed by H.-P. cylinder.. 66.33 I.H.P. 

31. Indicated horse-power developed by L.-P. cylinder. . 61.82 " 

32. Indicated horse-power developed by both cylinders. . 128.15 " 

33. Feed-water consumed by plant per indicated horse- 

power per hour, corrected for separator-water and 

for moisture in steam 15.60 lbs. 

34. Number of heat-units consumed per indicated horse- 

power per hour ... . 15,652.1 B.T.U* 

3$. Number of heat-units consumed per indicated horse- 
power per minute ' 260.9 " 



§ 43 2 TESTING PUMP1NG-ENG1NES. 633 

TOTAL HEAT OF STEAM RECKONED FROM THE VARIOUS TEMPERATURES OP 
FEED-WATER, AND COMPUTATIONS BASED THEREON. 

36. Total heat of 1 lb. of steam at 120 lbs. gauge-pressure, 

containing 1.5$ of moisture, reckoned from o° F.= 

i220.6-(i.5# of 866.7) 1,207.6 B.T.U. 

37. Ditto, reckoned from 215° temperature of main feed- 

water = 1207.6— 215.9 99*.7 " 

38. Ditto, reckoned from 225 temperature of low-pressure 

jacket-water = 1207.6 — 226. 1 981.5 " 

39. Ditto, reckoned from 290 temperature of high-pres- 

sure jacket and reheater water = 1207.6— 292.3 = . . 915-3 " 

40. Heat of separator-water reckoned from 340°= 353.9 — 

343-8 io.i *• 

41. Heat consumed by engine {H) = (18.863 X 991.7) + 

(615 X 981.5) + (815X915.3) + (210 X 10.1)= 20,058,150 " 

RESULTS. 

Substituting these quantities in the formulae, we have: 

a P p s L N 

1 n„tv - 3 ° 7 - 8 8 X (95 + 3 ' 6g + 4 ' 33) X 3 X 24>QQQ — 

1. Duty = — ■ X 1,000,000 

20,058, 1 50 
= 113,853,044 foot-pounds. 

C 

2. Percentage of leakage = — £ I44 ^ x 100=2.0$. 

307.88 X 3 X 24,000 

3. Capacity = 3< * 88 X 3 X 2 ^°° X U2 &\ 

10 
= 2,763,716 gallons. 

4. Percentage of total frictions 

a p p s 

307.88 x (95 + 3.69 + 4.33 ) 

A a M.E.P., A S2 MJE~P~: 2 l XI 00 

(307.88 X 59-25) + (1250.36 X 13.6) 
= 9-oJf. 



634 EXPERIMENTAL ENGINEERING. [§434- 

In the use of a system like the preceding, every precaution 
should be observed in the adoption of methods, as well as in 
taking observations. The water discharged by a -pumping- 
engine, for example, should never be obtained by computation 
from the measured dimensions of the pump and the observed 
number of strokes, but should be measured directly. A weir 
is commonly arranged for this purpose. Where the delivery 
of the pump has been actually measured, and the pump thus 
standardized, its use as a meter is less liable to error, but it is 
best avoided whenever possible. 

434. Standard Method of Testing Locomotives. — 
The following is a reprint of a report of a committee on 
standard methods of testing locomotives appointed by the 
American Society of Mechanical Engineers, and submitted at 
the San Francisco meeting in 1892 : 

Locomotive-testing is conducted under such unfavorable 
circumstances and surroundings that many of the exact methods 
employed in testing stationary engines or boilers cannot be 
used. It is desirable, therefore, that locomotive-tests be 
always made with a special train when possible, so that the 
same cars shall be used for the different trips, and the weight of 
train be uniform. The speed of the train can also be under 
control, and the tests not hampered by the rules governing a 
regularly scheduled train. Special and peculiar apparatus is 
employed by nearly every different experimenter as having 
some extra merit of convenience or accuracy, and we have 
endeavored to ascertain the best practical instruments and 
methods for the various measurements, and to illustrate or 
explain them. 

When a dynamometer-car is not used : 

As a final basis of comparison of locomotives, we recom- 
mend as a unit the number of thermal units used per indicated 
horse-power per hour. The object in view in testing a loco- 
motive will determine the methods employed and the extent 
and kind of data necessary to obtain. Some tests are made to 
ascertain the economy of a particular kind of boiler or fire- 



§434-11 TESTING LOCOMOTIVES, &ly 

box; others, the value of employing compound cylinders; 
others, to ascertain the relative merits of certain coals for 
locomotive use. 

As a practical and commercial unit the amount of coal 
consumed per ton-mile may be used. 

For a coal-test we give a separate method and test blanks, 
Form D, for tabulating results. 

For a unit of comparison of boiler-test we recommend the 
number of thermal units F. taken up every hour by the water 
and steam in the boiler. 

For a measurement of the resistance overcome in hauling a 
train, a dynamometer-car is essential, and we give a method of 
operating a dynamometer-car and of recording results. 

For a uniform method of recording results of indicator- 
tests, we recommend the blank Form A. 

For tabulating general results, Form B is presented. 

The waste from the injector should be ascertained by catch- 
ing it in a vessel conveniently attached, or by starting the in- 
jector several times in the engine-house and catching the over- 
flow in a tub. 

The total weight of the water caught divided by the num- 
ber of applications of the injector gives the average waste. 
The observer in the cab should keep a record of the number 
of times the injector is applied during the trips, and thus obtain 
data for estimating the total waste. 

FUEL MEASUREMENTS. 

The measurement of fuel in locomotive-tests is not difficult 
so far as a determination of the total amount shovelled into the 
fire is concerned. A weighed amount may be shovelled into 
the tank, and the amount remaining, after a given run, be 
weighed to determine the amount used, provided no water is 
used to wet down the coal. But it is next to impossible to 
determine the amount of coal used at any particular portion 
of a run when the coal is put in the tender in bulk. If coal is 
put in sacks containing 125 pounds each, with a small amount of 
"weighed coal on the foot-plate, even with heavy firing it is 



636 EXPERIMENTAL ENGINEERING. [§434- 

found quite possible for the fireman to cut open the bags, and 
dump the coal on the foot-plate as needed. In this way the 
rate of consumption on difficult portions of the run could 
readily be estimated. The use of water-meters and of coal in 
sacks obviates any need of weighing the tender, and thus re- 
moves one of the largest inaccuracies incident to the ordinary 
locomotive-tests. To determine the amount of coal used dur- 
ing the trip, it is only necessary to count the number of bags 
which have been emptied. However, the determination of 
the amount of fuel used during a run is not all that is neces- 
sary for a test. The measurement of the fire-line before and 
after a test is very essential and extremely difficult. If the 
run is a long one, then the errors in the determination of the 
fire-line may not be great ; but for short runs there seems to 
be no way of measuring the difference between the heat-value 
of coal in the fire before the test and after with sufficient 
accuracy to give reliable data. In tests made on a heavy 
grade, one trip closely succeeding another, it is of course im- 
practicable to drop the fire and measure the amount of fuel in 
the ashes remaining. Such measurements are unsatisfactory 
and inaccurate in any case, because it is not practicable to 
draw the fire without wetting it, as the ashes rise into the 
machinery, and they are too hot to handle. When one run 
succeeds another within a short space of time, some other 
method is necessary for measuring fuel used than by dumping 
the coal. 

The test is commenced with a good fire in the furnace, and 
the height of coal estimated by two or more assistants engaged 
in the trial. At the end of the run the fire should be in the 
same condition as near as possible. No raw coal should be in 
the box and steam-pressure and pyrometer-pressure falling. 

APPLICATION OF THE INDICATOR. 

If the power of the engine is to be determined, the action 
of the valve-gear examined, or the coal and water used per 
unit of power in a unit of time, the indicator must be used. 



§ 434- 



TES TING L O CO MO Tl FES. 



637 



This instrument should be attached to a three-way cock just 
at the outer edge of the steam-chest, in order that the con^ 
necting pipes (which should be { inch in diameter) can go 
directly in a diagonal direction to holes tapped into the sides 
of the cylinder rather than into the heads (Fig. 285). By this 
arrangement the pipes are shorter than when they pass over 




Fig 285. — Reducing-motion for Locomotives. 

the steam-chest into the heads, and have but short horizontal 
portions, thus facilitating the rapid draining of the pipes. 
Moreover, if a cylinder-head is knocked out th~ pipes are not 
dragged off, and the operator and indicator escape injury. 
The indicator should not be placed on horizontal pipes on a 
level with the axis of the cylinder-heads. 

The indicator-pipes and three-way cock should be covered 
with a non-conductor, wrapped with canvas and painted. The 
indicator itself should be wrapped as high as the vent-holes 
in its steam-cylinder. 



6 3 8 



EXPERIMENTAL ENGINEERING. 



[§434- 



The indicator-gear may be a rigid, true pantograph motion, 
either fixed or adjustable in height (Fig. 286) ; or it may be a 
simple pendulum connected by link to the cross-head with a 
wooden quadrant 2 inches thick, and having a radius such as 
will make the indicator-card 3 inches long. 

The cord of the indicator should be 8 or 10 inches long, 
and connected with a rod reaching forward from the panto- 
graph. 

In order to determine the steam-chest pressure, the indica- 
tor should be so piped that a steam-chest diagram can be 



Travel 3 




mid-position 

Rigid Non Adjustable 
Fig. 286.— Reducing-motion. 



drawn by it. A steam-gauge on the chest is inaccurate and 
difficult to use. 

Indicator-diagrams should be taken at equal distances in- 
stead of at equal time-intervals, in order to properly average 
the power. They should therefore be taken at mile-posts. 
The signal for taking diagrams should be given by the observer 
in the cab, who can pull a cord and ring a bell at the front of 
the engine, or blow the whistle. 

For the safety of the operator at the indicator, it is recom- 
mended that the seat be on a piece of boiler-plate above the 
cylinder, and so arranged that a piston or cylinder-head can 
pass out without injuring him. 



§ 434-3 TESTING LOCOMOTIVES. 639 

The person who takes the indicator-diagrams should be 
thoroughly sheltered by a temporary box containing a seat 
placed on the front end of the engine. Besides the usual indi- 
cator, there should be located near the observer a revolution- 
counter, which should be so arranged that after starting out 
the instrument will continue to record the revolutions for a 
period of exactly one minute, starting every time from zero, 
and when the minute has elapsed the counter will stop. Such 
an instrument is already in existence for taking the continuous 
revolutions of dynamos and high-speed engines, and little or 
no difficulty would be experienced in obtaining an instrument 
capable of taking the revolutions from some reciprocating 
part of the machinery. 

It is desirable also to have an electric connection between 
the indicator and the recording apparatus in the dynamometer- 
car, so that at the instant an indicator-diagram is taken, the 
fact may be registered on the dynamometer-diagram, see 
Article 181, page 246; and the cards should be numbered con- 
secutively, and the record likewise. 

Besides the person taking the indicator-diagrams, another 
person should be located in the cab of the engine, whose duty 
it should be to observe the point of cut-off given by the posi- 
tion of the reverse-lever, the position of the throttle-lever, and 
the boiler-pressure, all of which conditions should be recorded 
in a log-book for this purpose. 

Besides recording on the dynamometer-diagram the fact 
that an indicator-card is being taken, a bell should be rung 
at the same time, so as to call the attention of the observers in 
the dynamometer-car to this tact. 

LOCOMOTIVE-BOILER TESTS.— GENERAL DIRECTIONS. 

First. The drawing of the boiler to accompany the report of 
tests should be particular in specifying the construction in de- 
tail, with reference to coal-burning and generating steam, such 
as heating surface, grate area and the distribution of openings 
through the grate, volume of fire-box, size and thickness of 



64O EXPERIMENTAL ENGINEERING. [§434- 

flues, size of smoke-box, and the arrangement for draught, 
together with the thickness of walls between the heated gases 
and the water in the boiler ; the weight of the boiler itself 
should be given, and the number of cubic feet of water-space 
and of steam-space in the boiler, the division between the two 
to be taken at the middle of the range of the gauges. 

Second. Boilers for tests should be thoroughly cleaned on 
both sides of the heating surface, by a removal of the flues, 
before any test is commenced, and these surfaces should be 
kept clean by frequent washing during the test. 

Exception. — When it is desired to make a comparison of 
boilers for the purpose of determining a difference between 
them as to incrustation, they should first be tested as above 
when clean, and then tested again without cleaning further 
than the ordinary washing out of the boilers after the lapse of 
some months' service. The results are to be reduced to 
evaporation per square foot of heating surface ; both boilers 
using the same water during the period of testing. 

Third. In case the measure of the capacity of the locomo- 
tive boiler for generating steam be desired, without reference 
to the engines forming the locomotive, this capacity should be 
measured by the number of British thermal units, taken up 
per hour by the water and steam in the boiler, which may be 
readily determined from the observed data of temperature 
of water fed to the boiler, pounds of water evaporated per 
hour, and steam-pressure under which this evaporation occurs. 
Use any good set of steam-tables, such as Peabody's or Por- 
ter's, found in Appendix, or in Richard's Steam-engine Indica- 
tor. In such cases it will be necessary to specify all the perti- 
nent conditions under which such measure of the capacity of 
the boiler is made, so that in comparing with the capacity of 
another boiler all such conditions may be made as nearly alike 
as possible. It is, however, believed that a measure of the 
capacity of a locomotive boiler, without any reference to the 
capacity or efficiency and method of working of the engines 
on the locomotive which such boiler feeds, will not be of par- 
ticular value in comparison of boilers, unless the conditions 






§ 434-] TESTING LOCOMOTIVES. 64 1 

under which the entries are worked with different boilers are 
identical, or nearly so. 

Fourth. On account of the important influence which the 
temperature, and especially the moisture of the atmosphere, 
has upon the results obtained in a boiler-test, it is necessary to 
compare two or more boilers at the same place and at the same 
time, to get results which may be strictly comparable. The 
temperature of the air should then be noted for record. 

Fifth. To properly determine the amount of water fed to 
a locomotive boiler in service on a locomotive during any test, 
it is necessary to use a good water-meter, which should have 
its maximum error determined by previous tests and given 
with the report. 

Sixth. The coal used should be dry when weighed, and 
placed in sacks, each containing 100 or 125 lbs., care being 
taken to insure that all scales used are accurate. When an un- 
usually large amount of coal is needed, a weighed quantity of 
coal may be placed in the front of the tender and used first, 
and the test finished with coal from the sacks. An analysis of 
the coal used should accompany the report, which should 
show the volatile matter, the fixed carbons, etc., the moisture, 
and the ash contained in the coal. The ashes should be dried 
if they contain any moisture, and carefully weighed and re- 
corded after each test-run. 

Seventh. The temperature of the smoke-box gases should 
be measured by a good pyrometer, located near enough to the 
flues in the smoke-box to get the average temperature of the 
gases after they have passed the heating surface, and before 
they are mixed with the exhaust steam. It is suggested that 
pyrometers, such as that offered by Schaeffer & Budenberg, 
or Weiskopf, are suitable for this purpose. 

The location of pyrometers is shown in Fig. 288. 
These instruments cost about thirty-five dollars. They should 
register up to 1000 F. See Article 296. 

Eighth. The degree of exhaustion in the smoke-box should 
be measured and recorded by means of a simple manometer 
gauge. See Article 273. 



6 4 : 



EXPERIMENTAL ENGINEERING. 



[§434- 



Ninth. The quality of the steam furnished by the boiler 
to the engines should be determined by the most approved 
methods: See Chapter XIII. 

Tenth. Samples of gases passing from the flues to the 
smoke-box should be analyzed and results reported. The 




Fig. 288. 



means of taking such gases so as to insure perfect samples is 
to be further considered, and definite means prescribed. See 
Article 358, page 473- 



COAL TESTS. 



Directions to be observed in Supervising and Conducting Coal- 
trials. — The locomotive selected should be in good condition, 



§ 434-] TESTING LOCOMOTIVES. 643 

and either a new engine or one that has lately undergone 
repairs. 

The boiler should be washed before commencing the trial, 
the steam-gauge tested, the flues cleaned, and the exhaust 
nozzles cleaned and measured, which operations should be per- 
formed also whenever the kind of coal is changed. Instruc- 
tions should be given to round-house foremen that no repairs 
or alterations of any sort be made to the engine without the 
approbation of the conductor of the trial. The same engine- 
man and fireman should operate the engine throughout the 
trial, and the same methods of firing and running should be 
strictly adhered to. The run selected should be one in which 
the same distance is covered on each trip. The trains should 
be through trains and unbroken from end to end of the run, 
and the same number of cars and same lading should be pro- 
vided each trip. The same speed should, if possible, be pre- 
served on all trips. 

The conductor of the trial should be familiar with correct 
methods of firing and running locomotives, and should insist 
that the fireman adhere to approved methods of firing, and 
that the same method's be preserved throughout the duration 
of the trial, so that all coals shall receive the same treatment. 
(See Chapter XIV, on Heating Values of Fuels, and Chapter 
XV, on Steam-boiler Trials.) 

He should also see that the coal supplied at coaling points 
is of the proper kind, and should weigh the coal personally, and 
keep an accurate record of the following items : 

The coal consumed. 

The amount of ash. 

The amount of cinders in smoke-box. 

The water evaporated. 

The number of cars in train. 

The weight of cars as marked thereon. 

The weight of lading. 

The state of the weather. 

The direction and estimated velocity of wind. 

The temperature of the atmosphere. 



644 EXPERIMENTAL ENGINEERING. [§434- 

The temperature of the feed-water. 
The time on road. 
The steam-pressure. 
The exhaust-nozzles. 

The conductor should enter the above observations in a 
log-book, together with notes of repairs to engine, and any 
other items that might be of import. 

REPORT OF COAL-TRIALS. 

In order that coal-trials may be similar and consequently 
comparative, the following data should be observed (see Arti- 
cle 343, page 443) : 

First. 
Dates between which trials were conducted. 
Class of locomotive. 

Service in which trials were made, mentioning locality, etc. 
Name of conductor of trial. 

Second. 

Coal A. 
Kind of coal. 

Name of mine and operator. 
Location of mine. 

Physical quality of coal (appearance). 
Steaming quality of coal. 
Kind of fire made. 
Clinkers and ashes. 
Cinders in smoke box. 
Cleaning ash-pan and smoke-box. 
Labor involved in firing. 

Coal B. 
Same as above. 

GENERAL REMARKS. 

Comparison of evaporation (pounds of water evaporated 
per pound of coal). 



§ 434-] TESTING LOCOMOTIVES. 645 

Comparison of coal consumed per 100 tons hauled one mile. 

Value coal A, ioo#. 

Value coal B. 

Comparative value. 

Coal A is 100$ more or less valuable than coal B. 

A table of engine-performance and a table of general re- 
sults of engine-performance for each coal must accompany the 
report. (See Form D, page 646.) 

WATER-MEASUREMENTS. 

It has been found during the last year or two that meters 
are reliable and accurate within less than one per cent for 
measuring the water used by a locomotive. (The experience 
of the author does not accord with this statement — see Article 
214, page 284.) The meters should be specially made for the 
purpose and, if possible, free from any material that is injured 
by contact with hot water. They should be placed so as to be 
read from the cab. 

In mounting these meters, all pipes should be thoroughly 
cleaned before they are put into position, and a sufficiently 
large strainer should be placed between the meter and the tank. 
A most essential feature is to have a good flap check-valve be- 
tween the injector and the meter ; otherwise the hot water 
may flow backward and ruin the rubber recording-disks in the 
meter. As a check upon the meter, however, other means of 
measuring the water should be employed. The most convenient 
method is to use a float attached to a wooden bar which slides 
upon a graduated rod, the lower end of which rests upon the 
bottom of the tank. This rod is graduated to show 1000 lbs., 
and subdivided to 250 lbs. 

The method of graduating the rod is as follows : Fill the 
tank, place the bar and float in the proper position for read- 
ing, and mark the stationary rod zero at a level with the top 
of the float bar. Draw from the tank 1000 lbs., place the 
measuring device in position again and mark the rod, calling 
this mark 1. Again draw off 1000 lbs., mark the rod 2, and 
so continue until the water is all drawn. If the tank has a uni- 






646 



EXPERIMENTAL ENGINEERING. 



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§434-] TESTING LOCOMOTIVES. 647 

form horizontal section, several thousand pounds can be drawn 
off at once and the rod subdivided accordingly. 

In general the float is placed in the man-hole of the tank; 
but as this is not in the centre of gravity of the water-space, its 
readings are not quite correct if the two ends of the tank change 
their relative heights. This can be overcome by having a spe- 
cial small opening made at the centre of gravity of the tank, or 
as near it as possible, and using a small float. 

Another but less convenient way is to place a glass tube, 
on each side of the tank opposite the centre of gravity of the 
water-space, and to graduate scales behind them by the same 
method as above described. The objections to this method 
are the inconvenience in reading the scales (especially at way 
stations where there is but little time), their liability to freezing 
in cold weather, and the possibility of injuring them at any 
time. 

The float is always convenient and serviceable. 

When locomotive boilers are being fired hard, the water 
rises above the normal level, and a measurement of water just 
after the injectors have been throwing comparatively cold 
water into the boiler is not an accurate one ; the water shrinks 
and swells according as the firing is hard or as the locomotive 
is being worked. Hence measurements taken under these vari- 
able conditions are necessarily approximations. There is also 
a continuous movement of the water in the water-glass, and a 
mean of the oscillations is not quite satisfactory. Although 
the amount of water fed into the boiler can be determined ex- 
actly by the use of meters, yet the inaccuracies of the location 
of the water-line render water-measurements on short runs 
almost impracticable. The six-hour test for a stationary engine 
is considered satisfactory when successive tests will give the 
same results ; but in locomotive work, unless the engine be 
kept quiet, as it would be when tested in a shed, a short test is 
of little or no value. It may be accepted that a determination 
of the water-line by the sound of the gauge-cocks is too uncer- 
tain to be admissible in locomotive-tests unless the run is a long 
one. In such cases the total amount of water used is so large 



648 EXPERIMENTAL ENGINEERING. [§ 434- 

that any errors in estimating the water-level at the beginning 
or the end of the trip practically disappear. 

A locomotive which is undergoing a test should have a 
water-glass on the boiler. Behind this should be a strip of 
wood graduated, and surrounding the glass and fastened to the 
wood should be a copper wire at the height at which the water 
should be left at the end of every trip. The tank-measure- 
ment should not be taken at the end of the trip until the water 
in the boiler is at the standard height. The temperature of the 
water should be taken as it enters the tank at every station 
where water is taken, and tank reading should be taken before 
!ind after each filling. 

Leakage of Boiler. — To test for leakage, keep up the pres- 
sure to be carried, as nearly as possible, without blowing off, 
and note the fall of water in the water-glass in a given time, say 
four hours. Of course the injector must not be applied during 
this interval. The water-meter can then be used to determine 
the amount lost by leakage by reading the dial, applying the in- 
jector until the water reaches the original level, and then taking 
a second reading. The difference will be the amount of water 
lost. All boilers lose more or less from this cause, and if the 
test is to be a comparison between two different styles, the 
necessity for this information is obvious. 

* * * -x- * # * 

Before beginning a test, the pistons and the slide and throttle 
valves of the engine should be made tight. The point of cut- 
off for each notch of the quadrant should be ascertained, and 
the cut-off should be painted in white on the quadrant, or on 
boiler-jacket, with pointer or lever. All leaks about the engine 
should be stopped. 

A graduated scale and index should be attached to the 
throttle-rod to indicate its opening. 

A special steam-gauge with a long siphon should be used for 
the boiler-pressure and attached to t.he front of the cab at the 
left side, so that it will not become incorrect from overheating. 
Readings of the gauge, reverse quadrant, throttle-scale, and 
boiler-height-scale should be taken frequently, the first as often 



§434-] TESTING LOCOMOTIVES. 649 

as once in two and one-half, five, or ten minutes, depending 
on length and character of run, and all with each indicator- 
diagram, if the latter are being taken. 

Just before beginning a trip the water in the boiler should 
be at the standard height and the tank reading taken in order 
to ascertain the amount of water used while running, or per in- 
dicated horse-power per hour. 

Extraordinary efforts should be made to prevent blowing off 
before train time and while running. The number of times 
and the length of time safety-valve is blowing off should be 
recorded. 

No water should be taken from the tank for any purpose ex- 
cept supplying the boiler, and the boiler should not be blown 
off during a test if it can be avoided. If it cannot be avoided, 
the water should be at the standard height before and after 
blowing. 

DYNAMOMETER RECORDS. 

The dynamometer for measuring the resistance of the train, 
exclusive of the engine and tender resistance, should be able to 
record the following data : 

" A." — The pull upon the draw-bar. 

44 B." — The speed at which the train is running. 

" C." — The location of any point along the line used for ref- 
erence stations ; and possibly 

" D." — The wind-resistance. 

" A." — THE PULL UPON THE DRAW-BAR. 

The force required to move the train or the pull upon the 
draw-bar should be registered upon a strip of paper travelling 
at a definite rate per mile of distance travelled over by the train. 
The scale upon which this diagram is drawn should be as large 
as is possible within reasonable limits ; a scale of \ inch per 
IOOO lbs. pull is probably as suitable as any that can be de- 
vised, and the maximum registered pull need hardly exceed 
28,000 or 30,000 lbs. The height of the diagram should be 



>5° 



EXPERIMENTAL ENGINEERING, 



'% 434- 



measured from a base-line drawn upon the paper by a station- 
ary pen so located that when no force is exerted upon the 
draw-bar the base-line should coincide with zero pull. 



"B." — THE SPEED AT WHICH THE TRAIN IS RUNNING. 

This record should, if possible, be obtained in two ways : 

First. — By an accurate time-piece, preferably a chronometer 
furnished with an electric circuit-breaking device. It is of con- 
siderable importance that the time-piece should have its circuit- 
breaking device very carefully made, to produce exact intervals- 
of-time marks, because, when the matters of acceleration or re- 
tardation of speeds enter into the data required, it is important 
that the time-record should be correct. The question of length 
of intervals of time required is open to discussion. In most 
cases of ordinary work, five-second intervals, or twelve to 
the minute, are probably as satisfactory as can be decided 
upon ; for very careful work it would probably be advisable to 
have an auxiliary apparatus, something like the Boyer speed- 
recorder. 

Boyer Speed-recorder. — This instrument is constructed in 
such a manner that its accuracy and reliability are without 
question when it is properly mounted and cared for. It is not 
a delicate machine, and only needs ordinary attention. Its 
principle of operation is as follows : It consists of an oil- 
pump which works against a fixed resistance in the shape of 
an aperture through which the oil flows. The faster the 
pump runs, the greater is the pressure in the oil-cylinder. 
A piston in the oil-cylinder which moves against a spring 
rises in proportion to the increase of pressure. As the piston 
rises, a metallic pencil marks the movement on a roll of pre- 
pared paper, which moves in proportion to the longitudinal 
movement of the engine. In the cab is a dial which indicates 
at all times the speed of the engine with only a small error. 
The diagrams record all stops and make an accurate record of 
the rate of acceleration. 

Second. — It would be well to have, in addition to the 



§ 434-] TES TING LOCO MO TI VES. 6 5 I 

apparatus just described, another one which produces a con- 
tinuous curve upon the diagram paper, the ordinate of which, 
measured from a base-line, would give the speed in feet per 
second, or any other convenient measurement ; this could be 
obtained by modification of the Boyer speed-indicator. 



« C " — THE LOCATION OF ANY POINT ALONG THE LINE USED 
FOR REFERENCE STATIONS. 

These location-marks are most easily produced by having, 
at various convenient parts of the car, electric press-buttons, 
and having a pen upon the dynamometer which will be 
deflected sidewise when the circuit is made or broken ; this 
pen to be operated by an observer whose special duty it is to 
attend to this part of the work. 

" D."— WIND-RESISTANCE. 

Very little attention has so far been given to measurements 
of wind-resistance, or the relation it bears to the frictional 
resistance of journals and wheels, and few experiments on this 
subject are recorded. The subject is very complex, owing to 
the fact that it is generally supposed, and we think with good 
reason, that the train is so very largely surrounded by eddies of 
air, and that it will be very difficult to obtain any reliable data, 
especially when it is remembered that the clearances of a rail- 
road are greatly circumscribed and reduced to a minimum, so 
that it will be impossible to put any apparatus which measures 
resistance of this kind far enough out from the car to get 
reliable data. The apparatus for measuring this resistance 
would probably be subdivided into three separate disks, one 
facing front and two facing toward the sides of the car, all 
three connected together to produce a single resultant curve 
drawn upon the diagram paper, and the scale upon which this 
is drawn could probably be best subdivided into ten points, as 
practised by the United States Government. 



652 EXPERIMENTAL ENGINEERING. [§434- 



GENERAL. 

It is of very great advantage to have more than one relative 
speed on the paper upon which the diagrams are recorded, 
and the length of the paper consumed per mile run should 
bear some convenient relation to the distance travelled over. 

We would suggest that the rates of travel of paper per 
mile be such that 1 inch measured upon the diagrams shall 
represent 100 feet as the maximum, and that this distance be 
further subdivided so that \ inch shall represent 100 feet of 
track, and \ inch shall represent 100 feet of track. It is of 
course also necessary to have all of the registering pens located 
upon one line transverse to the direction of the movement of 
the paper, as in that way only can simultaneous data be 
recorded. 

The staff required to work the dynamometer is as follows : 

One chief, who has general supervision over the force, and 
whose duty it is to see that the records are properly obtained, 
and that all the location stations are properly marked upon 
the diagrams. 

One outlook, whose duty it is solely to observe the location 
stations, and to locate them upon the diagrams by means of an 
electrically moved pen. 

Besides this it is of considerable advantage to have a third 
person who is familiar with all the mechanism in the car, and 
who looks after the proper working of the mechanical parts oi 
the apparatus, and assists the general observer. 

TABLE OF ENGINE-PERFORMANCE. 

The following forms are recommended for tabulating the 
results of a locomotive-test, and in order to make the test com 
plete each test item should be entered. It is particularly im 
portant that the "equivalent evaporation from and at 21 2° per 
pound of coal " be entered, as it is only by this that evaporative 
comparisons can be made. 



§ 434 ] 



TESTING LOCOMOTIVES. 



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654 



EXPERIMENTAL ENGINEERING. 



[§434- 



Form B. 

LOCOMOTIVE-TESTS.— General Results. 

Railroad Co. 

Tests of locomotive No , between and 

Bound. . , 18. .. 

Distance, miles. Train No. . . , 

Kind of coal. Coal analysis Calorimetric value of coal. 



at 



Date 

Left 

Arrived " , 

Weather 

Mean temperature of atmosphere 

Direction of wind 

Velocity of wind, miles per hour , 

Condition of rail 

Size of exhaust-nozzle, single or double 

Weight of train in tons of 2000 lbs., including locomotive, tender, pas- 
sengers, and freight 

Weight" of train in tons of 2000 lbs., exclud. the locomotive and tender. 

Equivalent number of standard cars at tons each 

Maximum boiler pressure by gauge 

Minimum " " " 

Average " " " 

Prevailing position of throttle 

" " reverse-lever 

" points of cut-off 

Schedule time in motion 

Actual " " *' 

Time made up in minutes 

Aggregate intermediate stops, minutes 

Time during which power was developed, or throttle open 

Average speed, miles per hour 

Maximum number of revolutions per minute 

" rate of speed, miles per hour , 

Minimum number of seconds per mile 

Actual weight of coal used 

" " "wood " 

Average weight of coal burned per square foot of grate per hour 

Number of miles run per ton (2000 lbs,) of coal 

Number of pounds of coal used per mile 

Weight of ashes and unconsumed coal in fire-box and ash-pan 

" " unconsumed coal in fire-box and ash-pan 

" " cinders (sparks) in smoke-box 

" " combustible utilized 

Percentage of ashes and unconsumed coal in fire-box and ash-pan 

" " unconsumed coal in fire-box and ash-pan 

" " cinders in smoke-box 

" " combustible consumed 

Average temperature of feed-water 

Weight of water drawn from tender 

Waste of injector 

Weight of water evaporated (39-40) 

Actual evaporation per pound of total coal 

Equivalent evaporation from and at 212 per pound of coal 

" " '* " " " " " "combustible 

Coal used per ton of train per 100 miles. 

" " " car-mile 

Water used per ton of train per 100 miles 

" " " car mile 

" " " hour while developing power 

" " " " per square foot of heating surface 

41 " " " " " " " grate " 

Maximum indicated horse -power developed 

Average " " 

Total coal per indicated horse-power developed per hour 

Water evaporated per indicated horse-power per hour 

Dry steam used per I. H. P. per hour, per indicator-diagram 

Percentage of moisture in steam 

Average number of sq. ft. of heating surface per indicated horse-power, 

indicated horse-power per sq. ft. of grate surface 

Average temperature in smoke-box while using steam 

Prevailing vacuum " " " " " .. 



§ 434-] TES TING LOCO MO TIVES. 6$$ 

STEAM CALORIMETERS. 

There is little doubt that the throttling calorimeter will 
fulfil all requirements for testing the dryness of steam in 
locomotives. It cannot measure quantitatively more than 
about 5 per cent of moisture, but it appears probable that 
locomotive boilers develop steam which either contains a frac- 
tion of I per cent of moisture, or the priming is a sudden tem- 
porary action, causing water to mix with the steam to such an 
extent that no quantitative measurement of its amount is 
practicable. Under these circumstances all that is desired of a 
calorimeter is to indicate the temporary occurrence of this sud- 
den excessive priming, and a throttling calorimeter has been 
shown by Mr. D. L. Barnes to be capable of doing this, provided 
the thermometer has its bulb in direct contact with the steam 
flowing through the calorimeter. Such an arrangement is 
shown in the accompanying figure, of which the following is a 
description abstracted from the Railroad Gazette of November 
.27, 1 89 1 (see Article 330) : 

Calorimeter. — This instrument (see Fig. 289) consisted of 
two pieces of brass pipe, one inside of the other, leaving an air- 
space between the outer and the inner. The outer pipe was 
screwed into the dome and extended within the dome to the 
throttle. At this interior end the two pipes were joined together 
by a cap which had a perforation -fa of an inch in diameter. 
On the outer end of the inner pipe was placed a globe-valve, 
and next to this and outside of it a tee in which was a 
stuffing-box and a thermometer, as shown in Fig. 289. Be- 
yond this tee was another globe-valve and a short pipe of 
large diameter to carry the steam-jet away from the man in 
charge. 

With this device the point of most rapid movement of the 
steam was located next to the throttle, and any water coming 
near it would immediately pass through the opening because 
of the high velocity. The thermometer-bulb was bared to the 
steam, and no cups were used. It was found possible to shut 
off the outer globe-valve and expose the thermometer to a full 



*& 



EXPERIMENTAL ENGINEERING. 



[§ 435. 



boiler-pressure without blowing the thermometer from the stuff- 
ing-box. In this way it was determined that the thermometer 
recorded a steam-temperature which corresponded to the 
steam-gauge in the cab. 

With this instrument priming was shown whenever the 







Fig. 289.— Throttling Calorimeter attached to Locomotive. 



boiler was filled to a point where water could be seen coming 
from the stack. Immediately when the boiler foamed, the 
thermometer in the second calorimeter dropped to 21 2°. It is 
believed that this calorimeter is more accurate for locomotive 
Work, because it often happens that the locomotive primes 
only at starting and not for a sufficient length of time to en- 
able the throttling instrument to make a true record. And 
again, there are in a locomotive rapid changes in the rate of 
steam consumption which must cause rapid changes in the 
quality of the steam. 

435. Experimental Engines. — During the last few years 
many of the engineering schools have been provided with en- 



§ 435-] TESTING SPECIAL ENGINES. 657 

gines designed especially for experimental purposes. These 
engines do not resemble each other in any particular feature, 
but they do generally differ from the engines designed for 
commercial uses in the provision that is made for adjustment 
of the various working parts, and for varying the conditions 
under which the engine can be operated. Such engines are 
usually supplied with all the known devices for measuring the 
heat transmitted, the power received and that delivered from 
the whole or any part of the system. 

Space cannot be spared for the detailed description of any 
of these engines, but the following are the principal dimen- 
sions of the Sibley College experimental engine, shown as the 
frontispiece of the present work. 



GENERAL DIMENSIONS OF SIBLEY COLLEGE EXPERIMENTAL 

ENGINE. 

Diameter of high-pressure cylinder 9 inches 

" " intermediate-pressure cylinder 16 " 

" "low-pressure cylinder 24 " 

Length of stroke 36 " 

Revolutions per minute, 90. 

Diameter of fly-wheels 10 feet 

Width of face of fly-wheels 17 " 

Number of fly-wheels, 3. 

Diameter of brake-wheels 4 feet 

Width of face of brake-wheels 10 " 

Number of brake-wheels, 3. 

Diameter of high-pressure crank-pin 3^ *• 

Diameter of intermediate-pressure crank-pin 7 " 

Diameter of low-pressure crank-pin 3^ " 

Length of crank-pin 3^ " 

Length of connecting-rods 9 feet 

Diameter of main bearings 7 " 

Length of main bearings , 13 " 

Length of pillow-block bearings lo£ " 

Distance between centre lines of high-pressure and inter- 
mediate-pressure engines 14 feet 

Distance between centre lines of intermediate-pressure and 

low-pressure engines 12 feet 6 " 

Rated horse-power, 175. 

Floor-space occupied, 23 feet 9 inches X 31 feet 7 inches. 



6 S 8 



EXPERIMENTAL ENGINEERING. 



[§ 435- 



High-pressure Cylinder. 

Steam-ports f in. X 12 inches 

Exhaust-ports \\ " X 12 

Diameter of steam-valve seats 3^ 

Diameter of exhaust- valve seats s 3^ 

Thickness of steam-space in jacket £ 

Diameter of piston-rod 2^ 

Diameter of steam-inlet 3 

Diameter of exhaust-outlet 5 

Intermediate-pressure" Cylinder. 

Steam-ports 1 in. X 20 inches 

Exhaust-ports if " X 20 

Diameter of steam-port 5 

Diameter of exhaust-port 5 

Thickness of steam-space in jacket ^| 

Diameter of piston-rod 2^ 

Diameter of steam-inlet 6 

D' meter of exhaust-outlet 3 

Low-pressure Cylinder. 

Steam-ports , if in. X 28 inches 

Exhaust-ports 2-£ " X 28 

Diameter of steam-ports 6£ 

Diameter of exhaust-ports 6£ 

Thickness of steam-space in jacket , £ 

Diameter of piston-rod 2y\ 

Diameter of steam-inlet 6 

Diameter of exhaust-outlet , 8 






All the moving parts were weighed before they were put 
in place. 

The weights are as follows: 



Fly-wheels 20,807 

Brake-wheels 5,264 

Crank-shaft and eccentrics complete 9,958 

Total weight of crank-shaft, fly-wheels, brake-wheels, and ec- 
centrics 36,029 

Weight of high-pressure piston and cross-head 378^ 

Weight of intermediate-pressure piston and cross-head 503 

Weight of low-pressure piston and cross-head 790 

Weight of high-pressure connecting-rod 281 

Weight of intermediate-pressure connecting-rod 341 

Weight of low-pressure connecting-rod 282 



pounds 



i 



4350 



TESTING SPECIAL ENGINES. 



°59 



The connecting-rods were suspended on knife-edges, and 
the time of their vibration was taken as follows : 



Low-pressure 



High-pressure 



End on knife-edge. 



Time of 100 vibrations. 



sec. 



\ Crank end 4 ir 

Intermediate-pressure | c 



Cross-headend.. 4 " 44^ 

Crank end 4 min. 57! sec. 

" 41* " 

j Crank end .... 4 min. 44! sec. 

\ Cross-head end 4 " 45 " 



Receiver Dimensions. 



HIGH-PRESSURE RECEIVER. 

Length 11 ft. 7 

Diameter 14 

Number of tubes 15 

Diameter of tubes i£ 

Receiver volume 8.2 cu. 



ft. 



Seating surface 62.34 sq. ft. 



INTERMEDIATE-PRESSURE RECEIVER. 

Length lift. 7 in. 

Diameter :.... 20 " 

Number of tubes 19 

Diameter of tubes 2^ " 

Receiver volume 15.8 cu. ft. 

Heating surface 119. 8 sq. ft. 



The methods of testing experimental engines do not differ 
in any essential feature from those for testing any engine of the 
same general class. 



CHAPTER XX. 

EXPERIMENTAL DETERMINATION OF EFFECTS OF 
INERTIA ON THE STEAM-ENGINE. 

436. Inertia and its Effects.* — The effect of inertia of the 
moving parts of the steam-engine is to modify to a consider- 
able extent the resultant pressures which are transmitted by 
the connecting-rod to the crank-pin. The exact solution of 
this problem, including the effects of friction and gravity, has 
been accomplished by Prof. Jacobus and is published in the 
Trans. Am. Society of Mechanical Engineers, Vol. XI. Com- 
plete discussions of the effects of inertia will be found in 
various works devoted to the steam-engine ; also approximate 
methods, usually graphical, are given in these treatises which 
are sufficiently accurate for practical purposes. 

Prof. Jacobus gives the following formula for the approxi- 
mate calculation of the inertia-effects when friction and gravity 
are neglected, and when the rod is symmetrical about its centre 
line, and the path of motion of the wrist-pin passes through 
the centre of the crank-shaft. 

Let R equal radius of crank-circle; nR> length of connect- 
ing-rod ; ft, the crank-angle measured from its position when 
parallel to the centre line of the cylinder ; M, mass of the 
piston, piston-rod, and cross head ; m, the mass of the connect- 
ing-rod ; r, angular velocity of crank-shaft ; 6, connecting-rod 
angle; P n and P c , forces exerted by the connecting-rod upon 
wrist-pin and crank-pin, respectively; P a , pressure of steam on 
the piston ; T, tangential component of the force P c acting on 

* See Thurston's Manual of the Steam-engine, Vol. II., page 425. 

660 



§437-] DETERMINATION OF INERTIA. tt\ 

the crank-pin ; N, radial component of the force P e acting at 
the crank-pin ; Z and P b , auxiliary quantities. We have 

7 _ n 2 cos 2 6 - «'-sin a + sin 4 
_ ( n * _ sin 2 fl) 3 ' 

/>, = (M+ m)T*R(cos V + Z); 

T = (P a ~ P p ) sec./? sin (0+ fi) ; 
N = (P a - P p ) sec /?cos (0 + /?) ; 
P e =(P a -Ps) sec A 

When the accelerating forces are not included, 

r = P a sec/?sin(0 + /?); 
/>, = P a sec /?. 

In this work is discussed only the experimental method of 
determining the inertia of an engine as developed by Mr. E. 
F. Williams of Buffalo, N. Y., and published in the American 
Machinist in 1884 and '5. 

437. The Williams Inertia-indicator. — This instrument 
draws a curve (see Fig. 290) closely resembling the theoretical 
inertia-diagram, and similar in kind to an indicator-card. The 
horizontal length of the diagram corresponds to the stroke. 
The abscissa of any point of the curve identifies the position 
of the piston at a corresponding point in its travel, and its ordi- 
nate measures to a known scale the force required to give to 
a mass of known weight (one or two pounds) the acceleration, 
positive or negative, of the piston at that point of its stroke. 
The product of this force into the weight of the reciprocating 
parts, in pounds, gives for that point of stroke the positive 01 
negative horizontal force at the crank-pin due to the inertia of 
the parts. The instrument is shown in Fig. 290 attached to 
the cross-head of an engine, and in Fig. 292 in plan. 

The frame P is rigidly attached to the cross-head A hy two 
studs / and r, the former serving also as a pivot for the arm IJ. 
The upper end of B is pivoted to one end of a horizontal bar 
y whose other end is attached by a pin to some fixed support. 
In this way B swings back and forth, its lower end, together 



662 



EXPERIMENTAL ENGINEERING. 



l§ 437- 



n 



fQi 




Fig. agu— The Williams Inertia-instrument. Plan View. 




Fig. 29a.— Spring to Inertia-instrument. 
d 




Fig. 29a— The Williams Inertia-indicator. 



§437-] DETERMINATION OF INERlIA, 663 

with the frame P and the parts carried by it, travelling with 
the cross-head. Within the case or cage d (shown in section 
in Fig. 292) the weight h is free to slide horizontally on steel 
friction rollers, except as controlled by the spring. This spring, 
whose tension is known by calibration, is the only means by 
which the motion of the cross-head is communicated to the 
weight kj and it must therefore be extended or compressed by 
an amount which measures the force needed to overcome the 
inertia of the weight. 

For convenience h may be made to weigh, including the 
parts moving with it, exactly one pound. It is joined by a 
light rod e to the bent lever a which moves a pencil in a direc- 
tion at right angles to that of the cross-head motion. By the 
vibration of the arm B the paper is carried under the pencil 
on the curved platform b shown in Figs. 290 and 291. This can 
at pleasure be drawn upward by the cord m, and kept in contact 
with the pencil for one or more revolutions while the engine is 
in motion. The paper is put in place while the engine is at 
rest, and the neutral line x, Fig. 291, is drawn by swinging the 
arm B back and forth by hand. As soon as the engine is run- 
ning under the conditions desired, contact may be made and 
the diagram drawn. 

In using the instrument so as to make a diagram from 2 to 
3 inches long, the arm B may be varied in length to suit the 
stroke of the engine. To maintain a given average length of 
ordinates for widely differing speeds, the scale maybe changed 
by changing the spring, or the weight, or both. 

For obtaining the effect per pound weight of the recipro- 
cating masses, determine the scale as follows : The force 
exerted by an 80-lb. indicator-spring when it is compressed or 
extended \ inch, causing a pencil-movement of one inch, is 80 
lbs. per square inch of indicator piston-area. The latter 
being one-half square inch, the actual force on the spring 
is 40 lbs. If, then, an 80-lb. spring with a 2-lb. weight 
be used, a i-inch ordinate, will mean 40 lbs. exerted by thc 
spring in total, or a force of 20 lbs. per pound of the mass it 
moves. 



664 EXPERIMENTAL ENGINEERING. [§ 438. 

Thus a scale 20 means a force, for each inch of ordinate 
measured from the neutral line, equal to twenty times the 
weight of the moving body under investigation. In other 
words, each twentieth of an inch in length of ordinate repre- 
sents a force equal to the weight of the reciprocating masses. 

An 80-lb. spring with a i-lb. weight, scale 40 

" 80-lb. " " " 2-lb. " " 20 

" 40-lb. " " " i-lb. " " 20 

. " 20-lb. " " " I-lb. " " 10 

438. The Inertia-diagram drawn by the Instrument. — 

In interpreting the diagram several points are to be noted : 

1. The evenness and general form of the diagram are 
largely influenced by the smoothness of running of the engine, 
which depends on the accuracy of bearing surfaces, and the 
degree in which the weight of reciprocating parts, their veloci- 
ties, and the varying steam-pressures are suited to each other. 

2. The curvature of the lines traced depends chiefly on the 
ratio of crank-length to that of connecting-rod ; this ratio 
should be determined by measurement. 

3. In combining the diagram with an indicator-card the 
ordinates should represent forces in pounds per square inch of 
piston-area, and in the same scale as that of the indicator-card. 
For this we determine by independent measurement (1) the 
force exerted by the spring for a given length of ordinate from 
the neutral line ; (2) the ratio of the weight of the reciprocating 
parts of the engine to that of the parts of the instrument 
moved by the spring ; and (3) the area of the engine-piston. 

4. The difference in length of the corresponding ordinates 
in the inertia and indicator diagrams, the latter corrected for 
back pressure or compression, represents the net horizontal 
force transmitted to the crank-pin. 

For combination with a steam indicator-card, the force per 
square inch of piston-area is required. This is best obtained 
by getting the weight-ratio or the weight of reciprocating parts 
per square inch of piston-area. This multiplied by the scale of 
the inertia-diagram gives the engine-scale or scale of pounds per 



438-] 



DETERMINATION OF INERTIA. 



665 



square inch at the speed at which the diagram was taken. An 
example will make this clear. The inertia-diagram in Fig. 234, 
taken from a very smooth-running engine, was obtained with an 




Scale 40 
revs, per min. 

Hi" as 1Q" Porter- Allen 



Fig. 293. — Inertia-diagram. 




Scale 40 
265 revs, per min., 
4.416 " " sec. 



Fig. 294. — Inertia and Indicator Diagrams. 

80 spring and a one-pound weight. Hence the diagram-scale 
is 40. But for this engine the weight-ratio was 3. Hence 
40 X 3 = 120 is the engine-scale. 

Having, now, this inertia-diagram (Fig. 234) whose engine- 
scale is 120, suppose we are to combine it with an indicator- 
diagram (Fig. 235) from the same engine at same spe<vj, and 
taken with a 40 spring. The scale of the inertia-diagram can 



666 



EXPERIMENTAL ENGINEERING. 



[§ 438 



be changed from 120 to 40 by drawing it with the ordinate of 
each point increased three times, giving the curve ab in Fig. 
294. The ordinates to the compression curve on the back 
stroke can be deducted from the corresponding ordinates of the 
inertia curve ab, and the included area shaded, thus exhibiting 
the modification of the steam-forces by the inertia of the 
reciprocating parts. By vertical measurement of the shaded 
portion, the true distribution of horizontal forces on the crank- 
pin during the backward stroke may be obtained. 

Important Features of the Experimental Diagram. — Sup- 
pose that in Fig. 295 p and c are the positions respectively 




Fig. 295.— Relative Mosuott «f Crank-pin and Piston. 



of the cross-head and crank-pins with crank on its centre. 
Then, were it not for the angle of the connecting-rod, the 
cross-head pin would g. to /' when the crank has moved to 
\d' ,pp r being equal to oc\ 

But its true place is at p" ; thus in the quarter-turn of the 
crank from c to c" the cross-head has gone a distance p'p" 
past its mid-stroke, and is then moving at the same speed as 
the crank-pin, while its maximum speed was attained before 
reaching mid-stroke. Again, on the return-stroke, when the 
crank is lowest, the piston has not gone half-way. This shows 
that the acceleration is greater when the piston is at the head 



§438.] 



DETERMINATION OF INERT! 



667 



end of cylinder. The same thing is shown in Fig. 296, xy 
being much greater than x'y', while the fact that point of 
crossing of yy' and xx' is at the left of the centre shows that the 




Fig. 296.— Inertia-diagram. 

zero of acceleration, which of necessity corresponds with maxi« 
mum velocity, falls where it should. 




Fig. 297. — Inertia-diagrams. 

All this is revealed in the same way in the experimental 
inei lia-diagram Fig. 293, page 665, and the accuracy of the dia- 



668 



EXPERIMENTAL ENGINEERING. 



[§ 438. 



gram may be further tested by comparing the area below the 
neutral line with that above it by means of a planimeter. 

In Fig. 297 the inertia-diagrams for forward and backward 
strokes have been separated. The negative and positive signs 
show respectively where the inertia opposes and assists the 
steam-pressures. The curve y"y'" belongs to the forward 
stroke and y'y to the return. 

In practical use the diagram should be divided into ten or 
more equal spaces, and the ordinate at the centre of each 
space being numbered, the crank-positions corresponding, may 
be found as shown in Fig. 298, and the relative velocity of 




01 2 3 4 5 6 7 8 9 10 

7ig. 298. — Crank-positions corresponding to given Piston-positions. 



piston and crank obtained. The method of dividing the dia- 
gram shown in Fig. 297 is convenient in transferring the curve 
to a steam indicator-card similarly divided. Care being taken 
to draw both to the same scale and in pounds per square inch 
■of piston, the inertia curves may be drawn on an indicator- 
card arranged as shown in Fig. 299. Here the back-stroke 
steam-card has been drawn inverted and in contact with the for- 
ward card in its normal position, the two back-pressure lines 
being made coincident and used as the neutral inertia line. 



§438.] 



DETERMINATION OF INERTIA. 



669 



The ordinate lines are then produced to cut the line X X' ', 
which serves as a base-line from which to lay off ordinates of 
the net horizontal forces at the crank-pin. The actual forces 




Fig. 299. — Combined Diagrams. 



at the crank-pin are thus more clearly revealed for both strokes, 
and the areas above and below XX' respectively, give the actual 
work on the crank-pin for forward and return strokes. 



CHAPTER XXI. 



THE STEAM-INJECTOR— THE PULSOMETER 



439. Description of the Injector.— The steam-injector is 
an instrument designed for feeding water to steam-boilers, 
although it can be and often is used as a pump to raise water 
from one level to another.* It has been used as an air-com- 
pressor, and also for receiving the exhaust from a steam-engine, 



rw^m^ 




Fig. 300.— The Mack Non-lifting Injector. 

taking the place in that case of both condenser and air-pump. 
It was designed by Henri Jacques Giffard in 1858. 

In its most simple form (see Fig. 300) it consists of a steam- 
nozzle, the end of which extends somewhat into a chamber 
or converging tube called the combining or suction-tube ; this 

*See Cassier's Magazine, January and February, 1892 ; Thermodynamics, 
by D. Wood, page 279 ; Thermodynamics, by C. H. Peabody, page 152. 

670 



§ 43 9-] THE S TEA M-INJE C TOR— THE P UL SOME TEE. 6 7 1 

connects with, or rather terminates in, a third nozzle or tube, 
A (Fig. 300), termed the " forcer." At the end of the combin 
ing tube, and before entering the forcer, is an opening connect- 
ing the interior of the nozzle at this point with the surrounding 
area. This area is separated from the outside air by a check- 
valve, E, opening outward in the automatic injectors, and by a 
globe valve termed the overflow-valve in the non-automatic 
injector. The injector-nozzles are tubes with ends rounded to 
conform to the form of the " vena contracta " as nearly as pos- 
sible, and thus receive and deliver the fluids with the least pos- 
sible loss by friction and eddies. 

Some of the injectors are quite complicated, and adjust 




Fig. 301. — The Sellers Injector. 



themselves automatically by varying the openings through the 
tubes to suit changes in steam-pressure. 

Fig. 301 is a section of the Sellers injector of 1876; in this 
, injector the steam-nozzle C can be inserted a greater or less 
distance, as required, into the combining-chamber NN. The 
overflow P is closed by a valve K operated by a rod L con- 
nected to the starting-lever T. The tube NNCO moves 



672 



EXPERIMENTAL ENGINEERING. 



[§440. 



automatically to vary the opening at C with change of steam- 
pressure. 

In some of the injectors the tubes are so arranged that the 
discharge of one injector is made the feed for a second injector. 
This makes what is termed a double injector, of which familiar 
illustrations are to be seen in the Hancock, Park, and World 
injectors. 



JSTEAM 




OVERFLOW. 
Fig. 302.— The Hancock Inspirator. 



440. Thermodynamic Theory of the Steam-injector. — 

As a thermodynamic machine the injector is nearly perfect, 
since all the heat received by it is returned to the boiler, ex- 



§440-] THE STEAM-INJECTOR— THE PULSOMETER. 673 

cepting a very small part that is lost by radiation ; conse- 
quently the thermal efficiency should be in every case nearly 
100 per cent. Its mechanical efficiency, or work done in lifting 
water, compared with the heat expended 3 is small, because its 
heat-energy is principally used in warming up the cold water 
as it enters the injector. 

Let r equal the heat of evaporation in B. T. U. of a pound 
of dry steam; x, its quality; g, heat of the liquid of the 
entering steam in thermal units above 32 ; q 2 , heat of dis- 
charge-water in thermal units above 32 ; k, the total heat in 
a pound of wet steam ; w, the weight of steam per hour 
uncorrected for calorimeter-determinations ; W, the weight of 
water supplied ; t, the temperature of the feed-water ; t' ', the 
temperature of the delivery. Then we have, as the heat in 
one pound of the steam supplied, above 32 , 

h — xr-\- q (1) 

If the mechanical work consist of W pounds of water lifted n 
feet by pressure and s feet by suction, the heat equivalent F 
of the mechanical work is 

F^[(n+s)W+wn]A, (2) 

if delivered from the end of the discharge-pipe without sensible 
velocity. In case there is a velocity of v l feet per second at 
delivery from discharge-pipe, the additional energy Z, in heat- 
units, is 

L = A(W+w)v? + 2g. ..... (3) 

The heat-units taken up by the feed-water are 

K= W(t' -t) (4) 

The thermal efficiency E, if the injector is used for feeding 
toilers, is 

F - F + L + K «« 

W{/i - q t ) 



'674 EXPERIMENTAL ENGINEERING. [§44^ 

If used as a pump, the heat K received by the discharge-water 
is to be neglected, and the efficiency E P is 



E p = -^ + ^- (6) 

w(h — q,) l ' 



441. Mechanical Action of the Injector. — In this case we 
consider only the impact of the jet of steam at high velocity 
against the mass of water. The case being similar to that of 
a small inelastic ball, moving at high velocity, impinging on a 
large ball. 

Denote the velocity of the steam by v, that of the water 
before impact by V x , and after impact by V; then by the 
principles of impact of inelastic bodies, 

wv WV 1 _ (W-\-w)V 

g g~~~ g 7 

When water is supplied the injector under pressure, the 
sign of V l is positive, otherwise it is negative. The use of 
this equation requires the velocity of the steam, v\ that of the 
supply, V x ; and of the discharge, V, to be given. 

The velocity of the steam, v, will not differ essentially from 
1400 feet per second for the conditions in which it is used in 
the injector (see Article 230, page 301). 

The velocity of the water discharged, V, from the injector 
may be found by dividing the volume that is delivered in cubic 
feet per second, c, by the area of the discharge in square feet, 
A; that is, 

*-= 4 = ^X^=JL; .... (8) 

A 3600 a 2$a 



in which C represents the discharge in cubic feet per hour, and 
a the area of the discharge-nozzle in square inches. 



§ 44 1 .] THE S TEAM-INJECTOR— THE P UL SOME TER. 67$ 

The velocity of the water supplied, V 1 , in the suction-pipe 
maybe found by ascertaining the equivalent head, n 1 , that will 
produce the same velocity. If p be the absolute pressure per 
square inch in the combining-chamber ; b, the pressure per 
square inch, as shown by a barometer or pressure-gauge, on 
the water-supply ; w", the weight of a cubic foot of water at the 
temperature of the supply ; s, the suction-head in feet, — then 

I44(£ — p) , ,. 

». = w , — - * 5 (9) 

w 



V x = \ / 2gn l . 

The velocity of the suction is, however, expressed more con* 
veniently by considering a body of water with a head, s, acting 
to accelerate or retard the whole mass of water in the injector. 
Let A be the smallest section of the water-jet, w" the weight 
of a unit of water ; then the pressure due to s feet of water 
will be saw" . As this acts on a mass of water Vaw" ~ g, the 
velocity imparted would be 

saw" _sg 



Vaw" V 
g 

The total momentum produced by the suction would be 

W+wlsg\ I . W\ s , , x s t x 

in which 

y = JV-r- W. 

The momentum produced by the suction would be negative, 

jnless water was delivered to the injector under pressure. 

As shown in equation (7) the momentum of the suction is 

WV X W V V 

, which for one pound of steam would be x = y— 1 . 

Z ™ g g 



676 EXPERIMENTAL ENGINEERING. [§ 44& 

Substitute this value for the momentum of the suction in 
equation (7), representing W -r- w by y. We have 



or 



From which 



v = {i+y)(v~ S f). ..... (11) 



vV 

*+y = w=! g < I2 > 

The plus sign to be employed before s when the suction- 
water is supplied under pressure ; otherwise the negative sign is 
to be used. 

If the friction in the pipe be neglected, 

V= V2gn, 
and we have 



v V2gn , . 

y = 1. ...... hi\ 

' 2gn — sg v 0/ 



442. Limits of the Injector.— Maximum Amount of Water 

Lifted. — This may be obtained from equation (12) or (13), but 

it can be obtained with sufficient accuracy by neglecting the 

WV f 
momentum due to the suction-water in equation (7) ; in 

this case 

from which 

W v v 1400 , , v 

y = — = 77 — 1 = . — — 1 = . — — 1, nearly. (14) 



§44 2 THE STEAM-INJECTOR— THE PULSOMETER. 677 



The maximum ratio of water to steam is shown by the fol- 
lowing table : 



Delivery Pressure 


Maximum Ratio 


Delivery Pressure 


Maximum Ratio 


above that on 


of Water to 


above that on the 


of Water to 


Injector. 


Steam by Weight. 


Injector. 


Steam by Weight. 


IO 


36.5 


55 


15.5 


15 


29.8 


60 


14.7 


20 


25.6 


65 


14-3 


25 


23.8 


70 


13-7 


30 


20.9 


75 


13.3 


35 


19-5 


80 


12.9 


40 


17.87 


85 


12.6 


45 


17.0 


90 


12. 1 


50 


16.2 


100 


11. 5 

1 



The minimum amount of water required must be sufficient 
to condense the steam, in which case 



W h-q, 



y " w t' 



t' 



05) 



in which h is the heat in one pound of entering steam ; q 9 , the 
heat of the liquid in the delivery, both reckoned from 32 ; /', 
the temperature of the delivery ; /, that of the feed-water, so 
that the ratio cannot be greater than shown in equation (14) 
nor less than that shown in equation (15). 

Temperature of Feed-water. — As the temperature of the 
feed-water increases vapor is given off which increases the 
pressure, b, in equation (9) on the surface of the supply-water, 
and reduces the height through which the water can be lifted. 

If the temperature of the feed-water is greater, the amount 
required to condense the steam must also be greater; but as 
the amount lifted by a given amount of steam cannot exceed 
the approximate value given in equation (14), we shall have at 
the extreme limit at which the injector works, the values of y 
as given in equations 14 and 15 equal to each other, from 
which the maximum temperature of feed-water becomes 



* = *'- 



{hj-q^v 
v- V 



= t' 



1400 — 4/^ 



, nearly. 



678 



EXPERIMENTAL ENGINEERING. 



[§ 442'. 



The following table gives approximately the limiting values 
of suction-head in feet and temperature of feed-water : 

LIMIT OF SUCTION-HEAD IN FEET. 





Pressure of 


Limit of Suction- 


Steam-pressure 100 lbs. Absolute. 


Temperature 






of Feed-water. 


Vapor. Pounds 


head in case of 


Delivery 212 Fahr. 


Delivery 180 Fahr. 


Degs. Fahr. 


per sq. inch. 


Vacuum. Feet. 


Number of Pounds 
of Water to con- 


Number of Pounds 
of Water to con- 








dense one of Steam. 


dense one of Steam.. 


70 


O.36 


32.96 


7.04 


8.8l 


80 


O.50 


32.6 


7-57 


9.61 


90 


O.69 


32.2 


8.19 


IO.76 


IOO 


O.94 


31.4 


8.92 


12. II 


HO 


1.26 


30.9 


9.80 


13.84 


I20 


1.6? 


29.7 


10.87 


16.I5 


I30 


2.22 


27-3 


12,20 


19.32 


I40 


2.87 


25.9 


13.89 


24.22 


I50 


3-70 


24.8 


16.13 


32.3 


l6o 


4.72 


22.5 


19.23 


48.45 


I70 


5.98 


19.6 


23.81 


96.9O 


I80 


7-50 


16.9 


31-25 




I90 


9-33 


9-9 


45.46 




200 


11.52 


9-3 


83-33 




2IO 


14.12 


1.1 


500.9 





MAXIMUM TEMPERATURE FEED-WATER. 





Maximum Temperature of 




Maximum Temperature of 


Gauge Press- 
ure. Pounds 


Feed-water. 


Degrees Fahr. 


Gauge Press- 
ure. Pounds 


Feed-water. 


Degrees Fahr. 










per sq. inch. 


Discharge 


Discharge 


per sq. inch. 


Discharge 


Discharge 




180 Fahr. 


212 Fahr. 


70 


i3o° Fahr. 


212 Fahr. 


20 


142 


173 


109 


139 


25 


137 


168 


75 


I07 


137 


30 


133 


164 


80 


T o5 


134 


35 


129 


160 


90 


99 


129 


40 


126 


156 


100 


95 


125 


45 


123 


153 


HO 


91 


121 


50 


I20 


I50 


I20 


87 


117 


55 


117 


147 


130 


83 


"3 


60 


114 


144 


I4O 


80 


no 


65 


III 


141 


ISO 


77 


107 



§ 444-] THE S TEA M-INJE C TOR - THE P UL SOME TEE. 679 

A series of carefully conducted experiments* made at Sib- 
ley College, Cornell University, to determine the efficiencies of 
different steam injectors, confirm the results expressed in the 
preceding computations. 

443. Directions for Handling and Setting Injectors. — 
Injectors are of two general classes, lifting and non-lifting. In 
the first class water is drawn in by suction and then discharged 
against a pressure; in the second class water flows in under 
pressure and is discharged against a greater pressure. 

As there is a limit to the temperature at which water will 
be handled by the injector, variations in steam-pressure will 
affect the discharge and may cause it to stop altogether. This 
may be regulated to a certain extent by manipulating the 
valves of the steam and water supply ; some injectors are self- 
adjusting in this respect and are termed automatic. 

The general directions for starting an injector are to open 
the overflow, turn on steam until the water appears at the 
overflow, and the temperature of the injector is sufficiently low 
to condense the steam. Then close the overflow and the in- 
jector should discharge against a pressure equal to or greater 
than the steam-pressure. In many of the injectors the over- 
flow valve will open whenever the pressure in the injector 
becomes greater than that of the atmosphere. In several 
kinds the overflow is closed by a valve regulated independ- 
ently or connected by a lever to the starting handle so as to 
be opened and closed at the proper time by the simple opera- 
tion of admitting steam. 

Injectors will not work with oily or dirty water, and are 
liable to be stopped by anything that will not pass the nozzles. 
In general they are to be connected by pipe-fittings made up 
without red lead and arranged so as to deliver water into a 
pipe leading to the boiler, in which is placed a check-valve to 
remove the boiler-pressure when starting the injector. 

444. Directions for Testing. — For testing the injector 
use two tanks, both of which are to rest on weighing-scales. 

* See Cassier's Magazine, Feb. i8q2. 



68o 



EXPERIMENTAL ENGINEERING. 



[§444 



Fill one of the tanks with water, and locate the injector any 
convenient distance above or below this tank, and arrange it 
sc as to deliver water into the second tank. 

If the water that escapes at the overflow is arranged to run 
into the tank from which the water is taken, no correction will 
be requi/red ; otherwise it must be caught and weighed. 

Place a valve in the delivery-pipe, some distance from the 
injector or beyond an air-chamber, and regulate the delivery- 
head by partly opening or closing this valve. The delivery- 
pressure, which can be reduced to head in feet of water, can be 
measured by a pressure-gauge in the delivery-pipe ; the suction- 
pressure is observed in a similar manner by using a vacuum- 
gauge or a manometer. 

The water received, W, is that taken from the first tank ; 
the amount delivered, W-\- w, is that weighed in the second 
tank ; the difference is w, the steam used. 

Arrange thermometers to take the temperature of the 
water as it enters and leaves the injector. 

Make runs with discharge-pressures equal respectively to 
one-fourth, one-half, three-fourths, once, and one and one- 
fourth times that on the boiler. During each run take obser- 
vations, as required by the blank log furnished, once in two 
minutes. 

Determine the limits at which the injector stops working, 
for temperature of feed-water, suction-head and delivery-head. 

Careful trials show that the thermodynamic efficiency of 
any injector is ioo per cent ; by assuming this as true the sec- 
ond tank may be dispensed with, and the amount of steam 
computed from its heating effect and known quality on the 
water passing through the injector. 

In the report, describe the injector tested, explain method 
of action, and submit a graphical log, with time as abscissa, as 
well as an efficiency curve for varying pressures of discharge, 
also for varying temperatures of discharge. 

Fill out the log and make complete report, after the stand- 
ard form. 



§ 445-] THE STEAM-INJECTOR— THE PVLSOMETER. 



68 1 



445. Form for Data and Results of Injector-test. 



Cu 
V 

bf, 
■s 

"•5 

a* 

5 



Cu 

c 
«> s <-> 



a 



.0 u 8 



n v- e *- c 
H ~ Q c£ Q c£ 



cu > 
cu 
3 £ 



S ?. o 



o .2 



B a S £ e 
H H £ £ H 



682 



EXPERIMENTAL ENGINEERING. 



[§445- 



+ 



V 


* 


g 


+ 


+ 


E + 




* 


^ 


■H 




V 



X ^ 



4- 

k 

4- 


* + 






8 S 

CO *s, 

m o 

X 2 

o 




o 

8 i 





3 Is, 



s5 f< 



J PQ 



£ SB 



:=! H a 



r* 






Q 
O 
U 

II 
1^ 



£ ^ O 



54 I Vo 






a 






s s 



£ £ £ ao £ 



e a « 



w w U U > 



§ 44 6 -] THE STEAM-INJECTOR— THE PULSOMETER. 683 




446. The Pulsometer. — This is a pump consisting of two 
bottle-shaped cylinders joined together with tapering necks, 
into which a ball C is fitted so as to move in the direction o5 
least pressure, with a slight rolling motion, between seats formed 
in the passages. These chambers connect by means of open- 
ings fitted with clack-valves, E £, into 
the induction-chamber D. 

The water is delivered through 
the passage H, which is connected to 
the chamber by openings fitted with 
valves G. Between the chambers is 
a vacuum-chamber J which connects 
with the induction-passage D. Air is 
supplied the chambers by small air- 
valves moving inward, which open 
when the pressure is less than atmos- 
pheric. 

The method of working is as fol- 
lows : Conceive the left chamber full FlG - 303.-THE pulsometer. 
of water, and a vacuum in the right chamber; steam enters 
to the left of the valve C, presses directly on the surface of the 
water, and forces it past the check-valve G into the delivery- 
passage H and air-chamber J \ at the same time the right 
chamber is filling with water, which rushes in and by its 
momentum moves the valve C to the left. The steam in the 
left chamber condenses, forming a vacuum, and the operation 
described is repeated, except that the conditions in the two 
chambers are reversed. 

All the steam entering is condensed and forced out vith 
the water, increasing its temperature. 

The analysis is very similar to that of the injector, except 
that the steam acts by pressure instead of by impact. The 
theory is fully stated in "Thermodynamics," by Prof. DeVolson 
Wood, page 293. Thus: if w equal the weight of steam, W 
the weight of water raised, t the temperature of the supply, t x 
that of the delivery, r the latent heat of evaporation of the 



684 



EXPERIMEN TA L ENGINEERING. 



[§447- 



steam, T the temperature of the steam, n the delivery-head, 
n 1 the suction-head, n -\- n x the total head, — no allowance being 
made for variation, — we have 

w(T+r -t,)= W(t x -t). 
The heat equivalent of the mechanical work done, 

[7=A[Wn 1 +(W+w)n']. 
The heat expended, in thermal units, 

h = w( T — t -\- r). 
The efficiency, 

£ _U A[W7t 1 -\-{W+w)n-\ 
h w(T — t -\- r) 

Neglecting the work of lifting the condensed steam, 

r, A{n x + n) 



t x -t 



, nearly. 



The following form for data and results of test is used by 
the Massachusetts Institute of Technology : 

447. Form for Data and Results of Test on Pulsometer. 



No. 



Date, , 189. . 





a 


Flow of Steam. 


Water. 


Heads. 


Calorimeter. 


Counter 


u 

u 
xi 

s 

3 

Total 


3 

09 

to 

it 
ft 

ft 

u 

2£ 
"0 

n 


6 

u 
3 
10 
co 
V 

a 

(J 

S 




s 



3 
0, 

V 

0. 


<u 
<o 

a 


eo 

"a 

Ph 

■M 

d 
6 
u 
H 


a 
_c 

c 


X! 

a 

0) 

Q 


'53 

c 


A 

a 
u 

Q 


0) 

Q 

rtfr." 
. to 

IS 

5 bx 

H 


4) 
P 


O 



3 

en . 


& 

rt 

X 
O 

ds» 
a v 

go 




to 

c 

lT 

be 

3 

rt 
be 

c 

03 


to 
■J 

<u 
b<o 
3 
A ■ 

bxc 

x u 
cu 
to ^ 

s 


£ 

c 

.0 

u 

3 

a 

3 


c 
« 

V 

X 

a 

3 

< 


4; 
3 

CO 

CO 

CO 

ft 

I* 

xi 

'0 

m 


u 

3 
to 
<U 

ft 

<u 
4; 
6 
'C 


rt 
U 


CO 
HI 

eg 

bic 

D 

Q 

ft 
6 

H 


bi 
c 
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CS 

D 


y 

c 

V 
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s 


Av 








































Cor.. 








































\ 









































§447-] THE STEAM-INJECTOR— THE PULSOMETER. 685 

Diameter suction and discharge pipes „ ins. 

Transverse area of pipe sq. ft. 

Distance between pressure-gauges ft. 

Barometer (cor.) ins.; lbs. 

Number of pulses per minute 

Width of weir. ft. Area steam-orifice sq. ft. 

Steam used in mins. lbs. 

Water over weir in mins lbs. 

Head due to velocity in discharge-pipe ft. 

Total lift = pressure-heads -f- velocity-head -}- distance between gauges ft. 

Total work done by pulsometer ft. -lbs.; B. T. U. 

Total heat given up by steam B. T. U. 

Efficiency per cent. 

Duty (ft. lbs. per 1,000,000 B. T. U.) 



CHAPTER XXII. 

THE STEAM-TURBINE, 

448. General Principles of Operation. — The steam-turbine 
has come into extensive commercial use for the production of 
power during the last five years, and for that reason its theory 
and economic operation are matters of considerable importance. 

The steam-turbine is defined by Neilson as a machine in 
which a rotary motion is obtained by the gradual change of 
momentum of the working fluid. 

As constructed, the steam-turbine consists essentially of a 
rotating part carrying buckets against which the steam acts 
either by pressure or impulse or both, as with water-turbines as 
described on p. 316. The energy of the moving mass of steam 
is taken up by the rotating part and utilized to drive machinery. 

Dry steam if expanded adiabatically? and without doing work 
on anything but itself, through a divergent nozzle or one which 
does not interfere with its lateral expansion, will convert all the 
energy disappearing into velocity. If Q represent the heat per 
pound of entering, qi that of the discharge steam, and A = 778, the 
velocity produced may be calculated from the formula 

V 2 

— = A(Q-q). 

As an example, for the condition in which the steam enters at 
an absolute pressure of 285 pounds and is discharged at 0.6 
pounds absolute, the velocity of the steam calculated from the 

686 



§ 449-1 THE STEAM-TURBINE. 687 

preceding formula would be 4370 feet per second. The cir- 
cumference of the rotating part should move about one half 
that of the current of the steam which impinges on it, if the 
steam act on a single row of buckets, in order that it may be 
discharged with the least velocity and consequently with the 
least energy, which is a condition of maximum efficiency. If, 
however, there are a number of rows of buckets on the moving 
part which alternate with rows of fixed buckets on the stationary 
part of such shape as to deflect the current of steam in a direc- 
tion to propel the wheel at highest velocity, the circumference 
of the rotating part may move much slower than one half the 
velocity of the current of steam flowing at a rate which produces 
maximum efficiency. 

The steam-turbines of all types show a greater gain due 
to superheated steam than does the ordinary steam-engine; the 
Parsons turbine showing an increase in efficiency of about 1 per 
cent, due to an increase of superheat of 8 or 9 degrees up to at 
least 200 superheat. For best results the steam-turbines also 
require a high vacuum, and the specifications for steam-turbine 
installations generally require a high vacuum and a considerable 
degree of superheat. 

A large number of different types of steam-turbines * have been 
produced and many are in successful commercial use, but the 
limits of available space for this work permit the consideration 
of only two or three types in a brief manner. 

449. Steam-turbine of the Impulse Type. — The De Laval 
steam-turbine is an example of the impulse type. In this turbine 
a single wheel carrying a row of buckets near its periphery is 
acted upon by one or more jets of steam which are conveyed 
to the wheel through one or more expanding nozzles. (See Fig. 
304.) The wheel revolves in a case which is maintained at the 
pressure of the exhaust so that the steam expands very nearly 
adiabatically from the steam pressure to the exhaust pressure in 
the diverging nozzle, and before coming in contact with the 

* See Steam-turbines by Prof. Carl Thomas. New York, John Wiley & Sons. 



688 



EXPERIMENTAL ENGINEERING, 



[§449- 



buckets of the wheel. This velocity frequently reaches 4000 feet 
per second. 

The De Laval turbine, with steam entering at 4000 feet per 
second and with the nozzle set at an angle of 20 to the plane of 




Fig. 304. — The De Laval Turbine Wheel and Nozzles. 

motion of the buckets, should have theoretically a peripheral 
velocity for maximum efficiency equal to about 47 per cent of the 
velocity of the steam. The velocity of discharge for that condi- 




Fig. 305. — Sectional Plan op the De Laval Turbine Generator. 

tion it is claimed is 34 per cent of the initial velocity, and the 
energy absorbed by the turbine wheel is theoretically 88 per cent 
of that expended, making the steam consumption per theoret- 
ical horse-power 9.1 pounds per hour. 



§45°-] THE STEAM-TURBINE. 689 

Theoretically the peripheral speed of the De Laval turbine 
for highest efficiency should be about 1880 feet per second, but 
practically it is generally operated at 1350 feet per second, for 
best results, giving a horse-power for a theoretical steam con- 
sumption of 9.8 pounds per hour. On account of the high velocity 
of the steam-wheel of the De Laval turbine, it is necessary in 
applying the power to use a reducing-gear to lessen the speed of 
rotation. The diagram Fig. 305 shows a plan, partly in sec- 
tion, of the De Laval turbine with the steam- wheel near A, the 
reducing-gear wheels J and L, and couplings at M y which may 
connect it to a generator or other machine which may be driven 
at a high rotative speed. 

450. Steam-turbine of the Reaction Type. — The Parsons 
steam-turbine, shown in Fig. 307 in section, is an excellent illus- 
tration of a machine of the reaction type. In this turbine the 
rotating part consists of a steel drum which carries numerous 
rows of blades which move between stationary rows of blades 
supported by the casing surrounding the rotating part. 

The general arrangement of the blades is shown in Fig. 306. 
The steam is deflected by the stationary blades, P, so as to strike 

1 1 CC C (A ^Xi< C Stationary Blades 

2(_. J) J J J> rJ)) J) J) iMovimr Blades 



ft?' 
C C C C C (LCX C Statioil ( ar y Blades 



Moving Blades 



.1 ^ 

Fig. 306. — Blades of the Parsons Turbine. 

the moving blades, Pi, at the most effective angle, thence the 
steam is deflected to a row of stationary blades and thence again 
to a row of moving blades as shown by the arrows. Steam 
enters at A (Fig. 307) and passes in succession through the 
various rows of buckets on the parts F, G, H, and K. The last 
series of buckets are on an enlarged portion of the drum, O, which 
increases the volume and produces great expansion. From the 
rotating part it passes into the chamber, B, connected with the 
condenser. 



690 



EXPERIMENTAL ENGINEERING. 



[§45L 



To take the lateral thrust off the bearings, pistons or rotating 
collars, P, are arranged so as to receive the steam pressure and 
balance the thrust. 

The turbine is provided with a governor, L, which acts to 
turn the steam entirely on or off as may be necessary to maintain 
constant speed. 

The driving-shaft is extended for direct connection for an 




Fig. 307. — Parsons Steam-turbine. 

electrical generator for which the power generated by the turbine 
is generally used. The Parsons' steam-turbine is built by the 
Westinghouse Machine Co. and by the Allis- Chalmers Co. 

451. Steam-turbine of Combined Reaction and Impulse 
Type. — The Curtis turbine as built by the General Electric 
Co. is a good illustration of a combined impulse and reaction 
turbine. 

In this turbine the steam passes through a set of nozzles 
arranged in multiple; it then strikes the first row of blades, 
after which it reacts on alternate rows of moving and stationary 
blades as in the Parsons turbine. The general arrangement 
of the buckets in this turbine appears in Fig. 308, which shows 
the valves connecting the steam- chest with the supply nozzles, 
the development of moving and stationary blades, and the nozzle 
diaphragm through which the steam flows against another set 
of moving blades on a wheel of larger diameter. 



§452. 



THE STEAM-TURBINE. 



69I 



The number of stages may be made as great as necessary, 
there usually being four stages in large wheels. 

The large-size Curtis turbines are made of vertical form 
with a generator above the turbine and carried on the same 
vertical shaft, being supported below by a rotating collar resting 
on oil or water under pressure. The general arrangement is 
shown in Fig. 309, the generator being at G, the turbine at T. 
The steam-pipe is connected at 5, the exhaust-pipe at E. 



S'team Chest 




WIW1)1MWS)1)1)))D1)W Moving Blades ! 
Stationary Blades 
Moving Blades 




Moving Blades TO)TO)^DTOpPj£PPM 
Stationary Blades kC \.CjC\C-C, i C.CC^vC,\ \JC\CC,^^M 

• Moving Blades )W;W))W WW1)1M) ])1)U)\ 



Stationary Blades U «««««« «« <4<4 

Moving Blades 



Fig. 308. 



\ i I • j i I 

-Nozzles and Buckets, Curtis 
Turbine. 




Fig. 309. 



-The Curtis Turbo- 
generator. 



452. Testing of Steam-turbines. — Since there is a continu- 
ous flow of steam through the steam-turbine, at a uniform pressure 
and temperature for any one condition, there is no opportunity 
for taking a diagram similar to the indicator card, and conse- 
quently there is no means for measuring the mechanical work 
done by the entering steam on the rotating part. 

There may be, however, if the construction warrants, an 
opportunity of measuring the temperature and pressure at the 



6c 2 EXPERIMENTAL ENGINEERING. [§453- 

various stages in a multiple-stage turbine, and these quantities 
if possible should be observed. 

Most of the steam-turbines are constructed for direct con- 
nection to an electrical generator, and as usually built do not 
permit the attachment of intermediate thermometers and pressure- 
gauges. The test for that reason must generally consist in the 
measurement of the total steam and heat supplied and the work 
done by the generator. This latter is measured by means of 
various electrical instruments. If the efficiency of the generator 
is known, the work delivered (D.H.P.) from the turbine can 
be computed. 

From the heat input and the electrical output measured as 
described the efficiency can be computed on the basis of delivered 
or electrical horse-power. The heat (B.T.U.) per electrical or 
delivered horse-power supplied per minute can also be computed. 
These quantities are usually sufficient for all commercial require- 
ments and serve for a comparison of the results obtained with 
those of reciprocating engines, which are already well known 
from numerous tests. 

453. Log-sheets. — A log-sheet which suggests quantities to 
be observed and results to be computed in the test of a steam- 
turbine directly connected to an electrical generator is printed on 
the following page. The input H.P. is computed by adding all 
generator losses, reduced to horse-power units, to the output 
H.P. computed from the K.W. The thermodynamic efficiency 
is the ratio of the difference of temperature of steam centering 
and discharging, divided by the absolute temperature of the 
entering steam. The thermal efficiency is the ratio of the work, 
expressed in thermal units, AW, to the total heat supplied, Q. 
A perfect engine is assumed to be one that converts the differ- 
ence between the heat entering, Q, and that discharging, q, into 
work. 



§ 453-J THE STEAM-TURBINE. 693 

REPORT OF DIRECT-CONNECTED STEAM-TURBINE TEST. 

Made by Date 

Kind of Turbine Mfg. by 



Duration of run Hours 

Revolutions per minute 

Temperature of condensing water cold 

Temperature of condensing water warm 

Temperature of condensed steam 

Temperature of the engine-room 

Steam-chest pressure-gauge 

Barometer . . .inches Hg 

Condenser pressure " " 

Boiling temp. Exh. pressure 

Total steam per hr. condensed lbs 

Total condensing water per hr " 

Wt. condensing water per lb. steam. .'■ " 

Total heat supplied .B.T.U.— Q 

Total heat exhausted " — q 

Volts 

Amperes 

Series-field heat loss 

Shunt-field heat loss. . . : 

Armature heat loss 

Iron and friction loss 

K.W. hrs. useful output 

Total generator losses reduced to B.T.U 

Total input— H.P. (Calculated from K.W.) output 

Total D.H.P 

Efficiency of the plant 

Moisture in steam per cent 

Steam per input H.P. hr. (wet) lbs 

Steam per input H.P. hr. (dry) " 

Steam per D.H.P. hr. (dry) " 

Thermodynamic Eff (T-T') + T 

Tnermal Eff. . , AW+Q... 

Steam per H.P. hr. of perfect engine (dry) lbs. — (Q — q) -^-2545 

Ratio actual to theoretical water consumption 

Heat supplied per minute B.T.U 

Heat utilized per min . . ' * 

Heat discharged per min " 

Heat radiated per minute ' ' 



CHAPTER XXIII. 
HOT-AIR AND GAS ENGINES. 



454. Hot-air Engines. — Hot-air engines consist of engines 
in which the piston is driven backward and forward by the 
alternate expansion and contraction of a body of air caused by 
heating and cooling. Those now on the market are used prin- 




Fig. 311. Fig. 312. 

Ericsson Hot-air Pumhng-engine. 

cipslly for pumping-engines, and are arranged to use either 
coal or gas as fuel. 

455. Ericsson Hot-air Engine. — This engine is shown in 
Fig. 311 in elevation, and in Fig. 312 in section. 

694 



§45^-1 HOT-AIR AND GAS ENGINES. 695 

The method of operation is as follows : There are two 
pistons, viz., A, the displacing piston ox plunger, and B, the driv- 
ing-piston. The driving-piston is connected to the mechanism 
as shown. The displacing-piston, A, is a vessel made of some 
non-conducting substance, and its office is to move a body of 
air alternately from the space above to that below it. As shown 
in the figure, the piston A is at the upper end of its stroke, and 
the piston B is moving rapidly upward, being driven by the 
expansion of the air in the lower part of the receiver d. The 
air in the upper part of the receiver is cooled by water which 
has been raised by the pump r, and which circulates in the 
annular space xx. 

On the return stroke of the piston B the plunger A at first 
descends somewhat faster, and thus by transferring air main- 
tains a nearly uniform pressure upon the piston. When the 
piston B reaches the position shown in Fig. 312 on its down- 
ward stroke, the plunger A will be at the bottom of its stroke, 
and all the working air will have been transferred above and 
its temperature maintained at its lower limit, while it is com- 
pressed by the completion of the downward stroke of the 
piston B, after which the plunger will rise to the position 
shown in the figure and the temperature and volume are both 
increased at nearly constant pressure. The mass of air in the 
engine remains constant. 

456. The Rider Hot-air Engine. — In this engine the 
compression-piston A and the power-piston C work in sepa- 
rate cylinders, which are connected together by a rectangular 
passage D in which are placed a large number of thin metallic 
plates, forming the regenerator, whose office is to alternately 
abstract from and return to the air the heat in its passage 
backward and forward. The same air is used continuously ; it 
may be admitted to the cylinders by a simple check-valve O, 
opening inward. The engine is used entirely as a pumping- 
engine, and the water so raised circulates around the compres- 
sion-chamber B. 

The operation of the engine is briefly as follows : 

The compression-piston A first compresses the cold air in 



696 



EXPERIMENTAL ENGINEERING. 



§ 456.] 




Fig. 313.— The Rider Hot-air Pumping-engine. 



§ 45 8 -] HOT-AIR AND GAS ENGINES. 697 

the lower part of the compression-cylinder B, when, by the 
advancing or upward motion of the power-piston C and the 
completion of the down stroke of the compression-piston A, 
the air is transferred from the compression-cylinder B through 
the regenerator D and into the heater E without appreciable 
change of volume. The result is a great increase of pressure, 
corresponding to the increase of temperature, and this impels 
the power-piston up to the end of its stroke. The pressure 
still remaining in the power-cylinder and reading on the com- 
pression-piston A forces the latter upward till it reaches nearly 
to the top of its stroke, when, by the cooling of the charge of 
air, the pressure falls to its minimum, the power-piston de- 
scends, and the compression again begins. In the mean time, 
the heated air, in passing through the regenerator, has left the 
greater portion of its heat in the regenerator-plates to be picked 
up and utilized on the return of the air towards the heater. 

457. Thermodynamic Theory. — The thermodynamic 
theory of the hot-air engine will be found fully discussed in 
Rankine's Steam-engine and in Wood's Thermodynamics, 
from which it is seen that these engines may work under the 
conditions of change of temperature with either constant press- 
ure or constant volume, or under the condition of receiving 
and rejecting heat at constant pressure. 

The thermodynamic efficiency is found by dividing the 
range of temperatures of the fluid by the absolute temperature 
of the heated fluid. 

458. Method of Testing. — The method of testing hot-air 
engines does not differ essentially from that for the steam- 
engine. An indicator is to be attached so as to measure the 
pressures. Knowing the pressures and volumes, the corre- 
sponding temperatures can be computed from the formula 

£^ = Rz= 53.21, 
in which p is the pressure in pounds per square foot, v the 



6 9 8 



EXPERIMENTAL ENGINEERING. 



[§459- 



corresponding volume in cubic feet, and T the absolute tem- 
perature. From this 



T = 



pv 



The quantities which should be taken in each test are shown 
oc the following blank for data and results : 

459. Forms for Data and Results of Test of Hot-air 
Engine. 



MECHANICAL LABORATORY, SIBLEY COLLEGE, 
CORNELL UNIVERSITY. 



Test of Hot-air pumping-engine. Fuel, 

At 

Date 189. 



By 



Log of Trial. 



Symbol. 


h' 


w 


p 


/ 








2f 


t' 


*" 




iV 




G 




«/ 




Water. 


Pressures. 


Temperatures. 


Revolutions. 


Fuel. 


Leakage 


u 


i 


.• ! ^ 

, ho 1 •« 3 


(l 

Ok 






a 



P4 


*J 
(4 . 

u u 


Jacket. 


° 






u 

3 
O 

u 
V 

0. 


1 


3 


1 

3 
S3 


'53 '-3 

u 


^8. 


3 ST 


i 



£ si 

c e 
M 


rt hi 
<u c 


O 

E 

u 

0. 







































Average. 

RESULTS OF TEST OF HOT-AIR ENGINE. 
Data and General Results. 
Diameter of working-piston in.; Area of same 



. .sq. in. 
. .sq. in. 
. .cu. ft. 



Diameter of plunger in. ; Area of same 

Length of stroke, working-piston ft.; Displacement 

Length of stroke, plunger. . . ft. ; Displacement. .......... .cu. ft. 

Distance between centres of gauges ft. ; Zero of weir n. 



459-] 



HOT-AIR AND GAS ENGINES. 



699 



Head pumped against, feet , 

Average head over weir 

Water delivered, cu. ft. per sec 

" lbs. per hr 

" ie gals, per 24 hrs 

" " per hr. plunger-displacement 

Percentage slip 

Thermal units per lb. of fuel 

Average fuel-consumption per hour 

Heat from combustion per hour 

Duty per weir 

Duty per plunger-displacement 

Average M. E. P ,.. 

indicated H. P 

" effective " 

Efficiency, mechanical 

Total efficiency 

Expenditure of heat per hour 

Indicated work, B. T. U 

Heating jacket-water 

Radiation , etc 

Total. 



Symbol. 



H 

h 

% 

<2" 

Q'" 
X 

k 

G 

B. T. U. 

Duty 

M. E. P. 
I. H. P. 
D. H. P. 

E 

E' 



Determination. 



Remarks. 



The indicator-diagram obtained from the hot-air engine will 
depend largely on the principle of operation. The form of the 




Fig. 314. — Diagram from Ericsson Hot-air Engine. 



one obtained from the Ericsson engine in which there is change 
of temperature at constant pressure is well shown in Fig. 314. 



700 EXPERIMENTAL ENGINEERING. [§ 4^0. 

SPECIAL DIRECTIONS FOR EFFICIENCY-TESTS OF THE RIDER 
AND THE ERICSSON ENGINE. 

Rider Engine. 

Apparatus. — Steam-engine indicator with 16-pound spring; 
thermometers ; low-pressure gauge. 

Operation. — Build a fire in the heater; fill the jacket with 
water by priming the pump ; attach indicator ; place gauge 
behind the delivery-valve, and thermometers to obtain tempera- 
tures of water in supply and discharge pipes ; open delivery- 
valve and start engine by hand. 

Make five half-hour runs, increasing the head five pounds 
each time, and taking data every five minutes. To stop the 
engine, open fire-door and blow-off cock. 

Submit graphical log and plot efficiency-curve, using heads 
as ordinates and efficiencies as abscissae. 

Ericsson Engine, 

Apparatus. — Indicator with io-pound spring ; low-pressure 
gauge. 

Operation. — Light the gas under the heater ; place pressure- 
gauge behind delivery-valve, and attach indicator ; proceed 
with test and report as in efficiency-test of Rider compression- 
engine, beginning with a head of five pounds and increasing 
by five pounds up to twenty-five pounds. 

460, The Gas-engine. — The gas-engine is in many re- 
spects similar to a hot-air engine in which the furnace is 
included in the working-cylinder. 

There are many types of these engines now constructed, 
differing from each other in form, in methods of igniting the 
gas, and in the number of strokes required to complete a cycle 
of operations. In all these engines a mixture of gas and air, in 
such proportions as to be readily exploded, is drawn into the 
cylinder ; this is then exploded by firing either with an electric 
spark or with a lighted gas-taper, after which the piston is im- 
pelled rapidly forward, and the gas expanded ; the burned gas 



§ 4 6 °-] HOT-AIR AND GAS ENGINES. 701 

is then expelled from the cylinder before the introduction of a 
new charge. 

Gas-engines are usually single-acting, but a few have been 
made that were double-acting like a steam-engine. 

Dugald Clerk makes the following classification of gas- 
engines :* 

A. Engines igniting at constant volume but without previous 
compression, and of which the working cycle consists 
in — 

1. Charging the cylinder with explosive mixture. 

2. Exploding the charge. 

3. Expanding after explosion. 

4. Expelling the burned gases. 

Many of the early engines were of this type, of which may 
be mentioned those of Lenoir, Hugon, and Bisschof. 

A type of gas-engine in which the cycle is changed a little 
from that given was successfully introduced by Otto and 
Langen in 1866. In this engine the piston is shot forward by 
the force of the explosion in a long cylinder, while discon- 
nected from the motor-shaft, but on the return stroke it 
engages with the motor-shaft and completely expels the burned 
gases. 

The cycle is as follows : 

1. Charging the cylinder. 

2. Exploding the charge. 

3. Expanding after explosion while disconnected from the 

motor. 

4. Compressing the burned gases after some cooling. 

5. Expelling the burned gas. Work is done only on the 

return stroke. 
B. Engines igniting at constant pressure with previous com- 
pression, and of which the working cycle consists — 

1. Charging the pump-cylinder with the explosive mixture. 

2. Compressing the charge into an intermediate receiver. 

3. Admitting the charge to the motor-cylinder in the state 

of flame, at the pressure of compression. 

* The Gas-Engine, Dugald Clerk ; N. Y., J. Wiley & Sons. 



?02 EXPERIMENTAL ENGINEERING. [§4^0. 

4. Expanding after admission. 

5. Expelling the burned gases. 

To carry out this process perfectly the following conditions 
are required : 

(a) No throttling or heating from the air during admission 

to the pump. 

(b) No loss of heat of compression to the pump and 

receiver-walls. 

(c) No throttling as the charge enters the motor-cylinder 

or the receiver. 

(d) No loss of heat to the iron of the motor-cylinder. 

(e) No back pressure during the exhaust-stroke. 

The most successful engines of this type are Brayton's and 
Diesel's. 

C Engines igniting at constant volume with previous com- 
pression, of which the usual cycle of operations is — 

1. Charging the motor-cylinder with the explosive mixture. 

2. Compressing the charge in the motor-cylinder. 

3. Igniting the charge after admission to the motor. 

4. Expanding the hot gases after ignition. 

5. Expelling the. burned gases. 

To carry out this process perfectly the gases should not be 
heated until ignition, and they should not lose heat to the 
cylinder-walls during expansion; these are conditions in a 
measure contradictory and impossible to fulfil completely. 
The most successful engines now in use belong to this class, 
which is commonly known as the " four-stroke-cycle type," 
as it requires four strokes for each cycle of operation ; it was 
first proposed by Beau de Rochas in i860 and first practically 
applied by Otto in 1874. A modified form of the above type, 
known as the " two-stroke-cycle engine," requires but two 
strokes for the cycle of operation, the events taking place in 
the following order: 1 (out-stroke): Ignition; expansion; 
commencement of exhaust. 2 (in-stroke) : Completion of 
exhaust simultaneous with charging; compression. 

Compression engines were patented by Barnett in 1838 
and by Million in 1 840 with a different cycle from that described. 



§ 46o.] 



HOT-AIR AND GAS ENGINES. 



703 



Gas suitable for use in gas-engines is manufactured in a 
variety of ways and from a considerable number of substances. 
A mixture of hydro-carbon vapor and air is obtained by 
volatilizing some of the light hydro-carbon oils. 

The following table gives the composition and heating 
value of several different kinds of gases : 

COMPOSITION AND HEATING VALUE OF GASES. 



CO, percent. . . . 

H, " 

CH 4 , " .... 
C 2 H 4 , " .... 
CO a , " .... 
N, " 

O, " .... 

Vapor, " .... 
Weight per 100 

cu. ft., lbs 

B.T.U.percu.ft. 
B.T.U. per lb... 



Natural 
Gas. 
(Pa.) 



O.50 
2.18 
92.6 
0.31 
O.26 
3.61 
O.24 



4-56 

I IOO 

24150 



Coal Gas. 



A. 



8.18 
46.2 
34.0 
3.76 
8.88 
2.15 
0.65 

1-5 

3.2 

577 
17900 



6.00 
46.0 
40.0 
4.0 
0.5 
1-5 
0.5 



3-2 

735 
23100 



Water Gas. 



Enriched. Normal 



23.6 

35-9 

20.9 

12.8 

0.3 

3-9 

O.OI 

1.5 

4.6 

688 
14900 



45.oo 

45-0 

2.0 



4.0 
2.0 
0.5 



4-56 
322 
7120 



Producer Gas. 



Anthra- 
cite. 



27.O 

I2.0 

1.2 



2-5 

57-0 
O.3 



6.56 

137 
2IOO 



Bitumin- 
ous. 



27.O 
I2.0 

2-5 
0.4 

2-5 
56-2 

0.3 



6.59 
157 

2385 



Ignition in gas-engines is made to take place very nearly 
at the time of greatest compression. The various methods 
in use are (1) the open flame, (2) the hot tube, and (3) electric 
ignition of the contact and jump-spark variety. The ignition 
with open flame is accomplished by an auxiliary gas-jet which 
is constantly kept burning in a chamber adjacent to the 
cylinder, and which is put in alternate communication at 
suitable intervals with the atmospheric air and with the 
cylinder by means of a valve actuated by the engine. This 
method was used on the Barnett and the early Otto engines, 
but is seldom employed at the present time. 

The ignition with the hot tube is performed by connect- 
ing a closed tube, which is kept hot by an external flame, to 
the cylinder in such a manner that it will be filled during 
compression by the charge in the clearance. The charge is 



7°4 



EXPERIMENTAL ENGINEERING. 



[§ 460. 



fired by the heat communicated through the tube. Fig. 315 
illustrates the usual arrangement of a hot-tube ignition device. 

In this figure A is the cylinder, 
H the tube, G a gas-jet which 
plays around the tube H y dis- 
charging the products of com- 
bustion at B. In some con- 
structions communication be- 
tween the hot tube and the 
cylinder is closed by a valve 
except at the time of ignition. 
Electric ignition is of two 
kinds : the contact method, in 
which two terminals connected 
through a battery and spark 
coil are brought into contact 
within the cylinder and separ- 
ated rapidly, causing a bright 
spark by the self-induction of 
the coil. One form of this 
method of ignition is shown in Fig. 3 1 5^, in which the 
igniter terminal, a, is an arm mounted on a shaft, b, and 

Battery 




Fig. 315.— Ignition by the Hot Tube. 




Fig. 315a.— Wipe-spark Ignition. 

arranged to be worked by a suitable cam rod attached to the 
outer crank d. The terminal, e, is stationary and insulated 
from the cylinder-wall. The two terminals may be mounted 



§ 46o/ 



HOT-AIR AND GAS ENGINES. 



705 



in a removable plug P„ The extremities of the terminals 
should be of some metal, as platinum, that will resist 
the action of the electric current. Other forms of this 
method of ignition have a rubbing motion of the terminals 
before ignition. 

The other electric-ignition arrangement is illustrated 




Fig. 316.— Jump-spark Ignition. 



by Fig. 316. Both igniter terminals are stationary and 
mounted in a plug of insulating material, usually porcelain or 
lava. These are connected to the secondary terminals, s, s> 
of an induction-coil. The primary circuit of this coil is con- 
nected to a battery, B, at the proper moment by a contact 
cam on the secondary shaft, S. 

The primary circuit of the coil includes a vibrator, V, in 
many cases. With this arrangement a succession of sparks 
passes between the igniter terminals while the circuit-closing 
cam is in contact with its brush. In some cases, however, 
the vibrator is omitted, the circuit being broken only once, 
at the cam contact. 

The cut, Fig. 317, shows the construction of a recently 
designed four-stroke-cycle engine for gas or hydro-carbon 
vapor. In this engine, which is shown in section, the gas 
and air enter, through separate inlets, the mixing-chamber M, 
from which the mixture flows through the port N and inlet- 
valve J into the cylinder as the piston is beginning a down- 
ward stroke at the' commencement of a cycle of operation. 
The inlet-valve is opened once in two revolutions by the 
motion of the cam B, which makes one half as many revo« 



706 



EXPERIMENTAL ENGINEERING. 



[§ 46o. 



lutions as that of the main shaft of the engine. The charge 
is then drawn into the cylinder by suction. During the up- 




Fig. 317. — Section through Westinghouse Engine. 



stroke of the piston, the charge of gas and air is compressed 
in the cylinder. The charge is ignited by an electrical 
spark at about the time the compression is maximum and 
when both inlet- and exhaust-valves are closed. The ignition 
is performed by an igniter-cam arranged so as to bring two 
igniter-terminals into contact, completing the electric circuit, 
and then suddenly separating them by the energy in a coiled 



§ 46o.] 



HOT-AIR AND GAS ENGINES. 



707 



spring located in the guide D. The rise of pressure following 
ignition drives the piston downward to the end of its stroke. 




Fig. 318. — Section of Lozier Engine. 



On its return-stroke the exhaust-cam A opens the exhaust- 
valve E and the burned gases are expelled by the rising 
piston into the exhaust-pipe O. One cycle of operation is 
then complete and requires, as thus described, four strokes 
of the piston or two revolutions of the engine. 

For the purpose of cooling, a jacket is provided through 
which water is made to circulate, entering at H and dis- 
charging at K. In the engine above described the speed is 
regulated by a governor, not shown in the cut, which throttles 
the mixture of gas and air. 

A two-stroke-cycle engine is shown in Fig. 318, in which 
the cycle of operation is completed in two strokes or one revo- 



708 • EXPERIMENTAL ENGINEERING. [§ 460. 

lution of the engine, although the number of operations is the 
same as in the case of the four-stroke cycle. In the engine 
as shown in the figure, the mixed charge of gas and air is 
drawn into a chamber in the crank-case through the opening 
A, and is prevented from going backward by a check-valve 
opening inward which is located on the pipe supplying the 
charge. No valve other than the piston is employed to con- 
trol either the admission- or the exhaust-port. The admis- 
sion-port is in the lower part of the cylinder, at C, the 
exhaust-port is at the opposite side of the cylinder, at F. 
The charge enters when the piston is at the lower por- 
tion of its stroke through the open admission-port, due 
to the compression produced by the downward motion 
of the piston on the contents of the crank-chamber; at the 
same instant the burned gases are being exhausted through 
the open exhaust-port. On the return-stroke the fresh 
charge is compressed from the time the piston has covered 
the exhaust-port until the end of the stroke. The ignition 
is performed at about the time of greatest compression. 
We note that in this cycle of operation admission and 
exhaust take place simultaneously at the beginning of the 
upward stroke, and compression during the completion 
of the stroke; ignition takes place at or near the begin- 
ning of the downward stroke, expansion during the down- 
ward stroke, and beginning of exhaust near the end of this 
stroke. The advantages of this cycle of operation are 
claimed to be a greater number of impulses per revolution 
and a steadier motion for engines of the same weight. The 
disadvantages are the uncertainty of a clean cylinder for .the 
explosion and the probable loss of unburned gases in the 
exhaust, Actual tests show that the two-stroke- cycle en- 
gines are much less economical than those of the four-stroke- 
cycle type and fully as heavy per unit of power. 

455. Method of Testing Gas-engines — The method of 
testing gas-engines is in many respects the same as for a hot- 
air engine, but if possible measurement should be made of the 



§461.] HOT-AIR AND GAS ENGINES. 709 

vaporized and mixed with air, by a device called a carburetter, 
previous to its introduction into the engine cylinder. Engines 
designed for the use of gasolene are sometimes called "gasolene- 
engines," but they do not differ in any essential way from those 
designed for gas. The carburetter is always external to and 
independent of the engine, and is equivalent to a gas-machine 
in its results. Gasolene is the principal source of fuel for all 
portable or automobile motors, for which it is excellently suited, 
because of its great heating value per unit of volume and because 
of its easy volatilization in the carburetter without heat. Car- 
buretters are designed in various forms, but in all cases they 
provide means for passing the entering air over the necessary 
amount of gasolene while in a finely divided state. The regu- 
lation is frequently accomplished automatically by a float or other 
device. 

461. Oil-engines. — This name is appropriately applied to 
engines designed to use as a fuel the heavy petroleum oils which 
are not readily vaporized. These engines are internal-combus- 
tion motors, which differ from gas-engines principally in the 
fuel employed and in the means required for vaporizing and 
ignition of the same. They may be either of the two-stroke or 
four-stroke cycle type, but usually are of the latter. 

The first oil-engines used flame ignition, but those now built 
are ignited wholly or in part by the heat of compression aided 
by a hot tube, hot surface, or electric spark. The oil-engines 
are generally of the class which ignite at constant volume and 
during increase of pressure and temperature, the charge having 
been previously compressed. Prominent exceptions are the 
Brayton, which is not now built, and the Diesel. The Brayton 
ignites from a constantly burning flame at constant pressure 
during increase of volume and temperature. The Diesel ignites 
from the heat of compression at constant temperature during 
increase of volume and decrease of pressure. Oil-engines, it is 
noted, may be divided into three classes, igniting, respectively, 
(1) at constant volume, (2) at constant pressure, (3) at con- 
stant temperature. 



JiO 



EXPERIMENTAL ENGINEERING. 



[§ 46l 



In the Brayton the oil is sprayed directly into the cylinder 
during ignition, which takes place for a portion of the forward 
stroke. At the same time compressed air is supplied by a com- 
pressor, so as to maintain constant pressure in the working 
cylinder. The speed is regulated by a governor which controls 
the admission- valve for air and oil. The diagram from this 
engine is much like one from a Corliss steam-engine. 




Fig. 319.— The Hornsby-Akroyd Oil-engine. 



A n the Priestman oil-engine there is an external vaporizer 
heated externally by the exhaust gases, and through which the 
entire charge of oil and air for combustion pass on the way to 
the engine. 

In the Hornsby-Akroyd engine, shown in Fig. 319, the oil- 
charge is pumped into a chamber connected to the working 
cylinder, where it is vaporized by the heat. The air is drawn 
into the cylinder through a separate inlet- valve and forced by the 
compression into contact with the oil-vapor, causing ignition. 
The Priestman and the Hornsby-Akroyd in other respects resem- 
bles the Otto gas-engine. 



§ 462.] 



HOT-AIR AND GAS ENGINES, 



711 



462. Theoretical Relations of Pressure, Volume, and 
Temperature of a Gas. — The relations of pressure, p, volume, 
v, and temperature, /, of a unit of weight of a perfect gas during 
expansion or compression may be expressed by the following 
equations, in which T— absolute temperature, a = coefficient of 
expansion per degree of absolute temperature, a = number of 
degrees between freezing-point and absolute zero, po = pressure 
at o°, ^0= volume at o° of one unit of weight of the gas, and 
R = constant = poV a = poV Q /a. 

From Boyle's and Gay-Lussac's laws we have 



pv = poV (i+at); (1) 

• • (2) 



p v = ^T=^(a + t)=R(a + t)=RT, 



pv=RT may be considered the characteristic equation of a per- 
fect gas since it shows the relations, during expansion or com- 
pression, of a unit weight between the pressure, volume, and abso- 
lute temperature. R is a constant dependent on the nature of 
the gas, with values as follows for a few of the gases : 





Values of R. 


English Units. 


Metric Units. 


Hydrogen (H) 


770.3 
48.74 

35-41 
53-22 


422.68 
26.475 
iQ-43 
29.20 




Carbon dioxide (C0 2 ) 

Air 





Expansion and compression may take place (1) isothertnally, 
in which case there is no change of temperature, or (2) adiabat- 
ically, in which case there is no increase or decrease in the total 
heat. For the first case, since the temperature remains constant, 



pv = p'v r . 



(3) 



The curve corresponding to this equation is an equilateral hy- 
perbola asymptotic to the axes of volume and pressure. Methods 



7 12 EXPERIMENTAL ENGINEENING. [§ 462 

of drawing this curve have already been given in Art. 404, pages 
554 and 555. 

For the second case, or adiabatic expansion or compression, 



«$■ 



from which 



ptfVo k = pv k = a constant, (4) 



in which k = c P /c v . c P = specific heat at constant pressure and 
c = specific heat at constant volume. 

During adiabatic expansion the relations of temperature and 
volume are shown by the following equation: 

V) =T & 

The relation of pressure and temperature by 

1— k z—k 

Tp k =T 1 p 1 k . ( 6 ) 

The following table (see next page) from Clausius (Mechanical 
Theory of Heat) gives the value of the two specific heats for a 
few of the gases. 

The adiabatic curve may be drawn when po, v , and k are 
known by assuming values of v and calculating, either with a 
table of logarithms or a slide- rule, corresponding values of p. 

The mechanical work, W, done during isothermal expansion 
between the volumes v 2 and v± is theoretically as follows: 

/f V2 dv v 2 

pdv = p 1 v 1 J^ — = ftvilog,— . ... (7) 

The work done during adiabatic expansion from v 2 to Vi is 
as follows: 

-en-fen « 



§4^3. 



HOT-AIR AND GAS ENGINES. 



713 



Name of Gas. 



Air 

Oxygen 

Nitrogen 

Hydrogen 

Nitric oxide 

Carbonic oxide. . . 
Carbon dioxide. . . 

Steam 

Disulphide carbon 

Olefiant gas 

Ammonia 

Alcohol 



Symbol 



O 

N 

H 

NO 

CO 

co 2 

H 2 

cs 2 

C 2 H 4 
NH 3 
C 2 H fi O 



Specific Heat. 



Constant 
Pressure. 



2375 
2I 75 



2438 
4090 

2 3*7 
2450 
2169 
4805 

x 569 

0.4040 
0.5084 
o-4534 



Constant 
Values. 



O.1684 

o-^S 1 
o. 1727 
2.4110 
o. 1652 

0.1736 

o. 1720 

0.3700 

o. 1310 

0-3590 
0.3910 

0.4100 



406 

403 

416 

414 

402 

413 

261 

298 
198 

J 25 
3OO 

!5 



The heat applied during isothermal expansion or received 
during isothermal compression is given by the following equation: 

/ V2 dv Vo 

-=(^- Cs )r 1 io ge -, 



or 



Q=ART 1 log.^-Ap 1 v 1 log.^ i . 



(9) 



The complete derivation of these equations can be found 
in any work on thermodynamics; they are given here merely for 
convenience. 

463. Cycle of Operation of Gas-engines. — A body is said 
to operate in a closed cycle when it returns to its original state after 
passing through a series of physical and chemical changes. When 
a change of composition occurs, as is the case during combus- 
tion in the internal- combustion engine, the body may return to 
its initial condition only so far as pressure and volume are con- 
cerned and not in other respects. For this reason the gas-engine 
operates in a cycle which is only approximately closed. 

If <2=heat received, q that exhausted, the highest possible 



7H 



EXPERIMENTAL ENGINEERING. 



[§ 464. 



maximum efficiency would be for that condition (Q — q)/Q, which 
ratio has been called by A. Witz the "coefficient of economy." 

The Carnot cycle is an ideal one which differs materially from 
any actual cycle of the gas-engine, yet it is useful as a basis of 
comparison, since it represents the maximum return in work 
for a given fall of temperature. In this cycle there is isothermal 
and adiabatic expansion followed by isothermal and adiabatic 
compression. For this case it can be shown that 

Q-q T-T 



in which T is the absolute temperature during the isothermal 
expansion and T' that during isothermal compression. 

The thermal efficiency may be calculated from the I. H. P. 
by dividing the mechanical work shown by the indicator diagram, 
expressed in heat-units, by the heat value of the fuel consumed. 
It may also be expressed as the ratio of the delivered work in 
heat units to the heat value of the fuel. Thus if T^ = the mechan- 
ical work delivered, IW the mechanical work shown by the 
indicator diagram, then will the efficiency be as follows: 

Thermal from I. H. P. =IW/Q; 
Thermal from D. H. P. =W/Q. 

464. Method of Testing Gas- or Oil-engines. — The 

method of testing gas- and oil-engines is essentially the same, the 
difference being principally due to the different methods of 
measuring the gaseous and liquid fuel. The object of the test 
in every case is to find the relation of the work performed to the 
thermal value of the fuel supplied, and the efficiency of the engine. 

To obtain these results the amount of air should be ascer- 
tained. This may be computed approximately by subtracting 
the volume occupied by the fuel from the cylinder displacement, 
but it is desirable whenever possible to meter or measure the 
entering air. 

In attaching the indicator it will be found necessary to use 



§ 464.] 



HOT-AIR AND GAS ENGINES. 



715 



a heavy spring in order to resist the effect of the explosion. 
This spring, because of its stiffness, will show but little work on 
the intermediate strokes; for this reason it is advisable to use a 
second indicator with a light spring, in which is placed a stop 
for the piston so that the spring cannot be compressed to such 
an extent as to injure it. A pyrometer should be inserted in 
the exhaust, and a gas-bag placed between the gas-meter and 






Gas 

Meter 



^yiomeW 




Fig. 320. — Plan of Arrangement for Gas-engine Trial. 



the engine. The proper arrangement of a gas-engine for trial 
i? shown in Fig. 320, from Thurston's Engine and Boiler Trials. 

The heat-units per cubic foot of gas used should be deter- 
mined by a calorimetric experiment (see page 451). The actual 
and ideal indicator-diagrams are shown in Fig. 321, the differ- 
ence being in great part due to losses of heat in the cylinder. 

The report of the test should contain a description of the 
engine, the method of testing, together with the log and the re- 



716 



EXPERIMENTAL ENGINEERING. 



[§ 464. 



suits properly tabulated. In connection with the test of a gas- 
engine, plot a curve with cubic feet of gas per I. H. P. at 32 F. 
and atmospheric pressure as ordinates, and I. H. P. as abscissae. 

In the test of gasoline- or oil-engines, plot a similar curve, 
using the weight of fuel instead of the volume of gas. 

Also plot a curve showing the relation of the total B. T. U. in 
the fuel supplied to the total I. H. P. and D. H. P. of the engine. 



Mean pressure 46o5 

P.e-voluUons p.ermln, 18<W50 
Eiplosioms 4> »* 12<W 
XJB.JE. Total 




4o**oa 0.2 0.3 ba ois 0:6 o;7 

OTTO ENGINE. ATKINSON ENGINE. 

Fig. 321. — Actual and Ideal Indicator-diagrams from Gas-engines. 



In case the air cannot be directly measured it may be approxi- 
mately computed in the case of the oil-engine by obtaining the 
ratio of the weight of oil to the weight of air required for the 
cylinder displacement. 

In the test of the engine the temperature of the exhaust gases 
is obtained which is less than the temperature during the 
exhaust stroke existing in the cylinders. The amount of this 



§ 465.} 



HOT-AIR AND GAS ENGINES. 



717 



difference is now known. Assume that it is 50 and compute 
from the theoretical formula which gives relation of p, v, and T, 
Art. 462, the temperature at the beginning and end of the stroke. 



120- 








110 






K 


100 


\ 




s 




\ 


90- 


N 




\ 


80- 


Is \ 




1 


i \ 






\ \ 


•70- 


' 


\ \ 


00- 


i 

1 


\ \ 


50- 


1 




40- 


! \. \„ 


30 


- 'K^^/^^ 




,20- 




4 


10- 


. 1 Atmospheric Line 







1 1 V " v i 





! ° 






Zero Pressure 





4]Atmos. Line 



Fig. 322. 



465. Data and Results of Test. — The following form gives 
the data and results of test for a gas-engine. 

In case of the test of an oil-engine the items relating to the 
weight, volume, and thermal value of gas are to be changed for 

the corresponding items respecting the weight, volume, and 
thermal value of the oil which is employed as a fuel. 

Fig. 322 shows in heavy lines the actual indicator-diagram 
from a four-cycle gas- or oil-engine; the work done during the ex- 
haust and charging strokes is shown to a large scale in the lower 
part of the figure. The dotted line shows the theoretical diagram 
for the same conditions. 



18 



EXPERIMEN TA L ENGINEERING. 



[§ 465. 



Data and Results of Test of Gas Engine 

By 190 

Object of Test , 



Dimensions of Engine. 

Rated H.P. at R.P.M.= 

Diameter of piston In. 

Area of piston Sq. in. 

Length of stroke Ft. 

Piston displacement Cu. ft. 

Clearance Cu. ft. 

" Per cent 

Diameter piston-rod In. 

' ' crank-pin In 

Scale of indicator spring Lbs. per in 



Data. 



Run No. 


I 


II 


III 


IV 


Duration trial, hrs 










Brake load, net lbs 










Gas, total cu. ft 










*Gras per hour, cu. ft 










Air, total cu. ft 










*Air per hour, cu. ft 










Ratio air to gas by weight 










Jacket-water, total lbs 










' ' per hour, lbs 










' ' temp, entering, F° 










" ' ' leaving, F° 










' ' range, F° 










Revolutions, total 










' ' per hour 










' ' per min 










Cycles, per min 










Explosions, total 










' ' per hour 










' ' per min 








































1 ' range 




















*Air, wt. of a cu. ft., lbs 










*Mixture, wt. of a cu. ft., lbs 










Specific heat, gas 










' ' air 










' ' exhaust gases. 










*Thermal equiv., cu. ft. gas, B.T.U 





















* At 3 2 F. and 14.7 lbs. absolute pressure per sq. in. 



§ 465-] 



HOT-AIR AND GAS ENGINES. 

Results. 



719 



Run No. 


I 


II 


III 


IV 


INDICATOR. 

Maximum press, lbs. sq. in 










Compression press, lbs. sq. in 










M.E.P. power stroke 










' ' comp. " 










I.H.P. net 










D.H.P 




















Mechanical efficiency, per cent 










Weight of gas per hr., lbs 










Weight of air per hr., lbs 










*Gas per I.H.P., per hr., cu. ft 










" " " " lbs 










" " D.H.P., " cu. ft 










" " " " lbs 










HEAT PER HOUR. 

Supplied B.T.U. 










" Per cent 










Absorbed by jacket-water B.T.U 

" Percent 










Exhausted B.T.U. 




















Thermal equiv. Ind. work B.T.U. 










" Percent 










Radiation and loss B.T.U. 




















Thermal units per I.H.P. per hr 










" " D.H.P. " " 










EFFICIENCIES, PER CENT. 
Possible thermal= • ■ 










Thermal from I.H.P 










" D.H.P 










.-, J- max J- min 

Carnot= — 










1 max 











* At 32 F. and 14.7 lbs. absolute pressure per sq. in. 



CHAPTER XXIV. 
AIR-COMPRESSORS. 

, 466. Types of Compressors.— Compressed air is used 
extensively in the various mechanical arts for the purposes 
of ventilation, operation of motors, tools, the transmission of 
energy, and refrigeration. There are three types of air-compres- 
sors, viz.: (1) the piston, (2) the rotary, and (3) the centrifugal 
blower or fan. They may be driven by any convenient motive 
power, as, for instance, a steam-engine, as shown in Fig. 325, 
a water-wheel, an electric motor, etc. 

467. Piston Air-compressor. — In this machine the air 
is compressed by a piston moving in a cylinder which is pro- 
vided with inlet- and exit-valves. The valves are commonly 
operated automatically by the entering or discharging air, but 
in some cases they are positively operated by mechanical means. 
A section of an air-compressor cylinder with automatically 
operated valves of the poppet- type is shown in Figs. 323 and 
324. In Fig. 323 the inlet-valves are shown in the cylinder 
walls, in Fig. 324 they are shown in the piston, which commu- 
nicates with the air by the hollow inlet-pipe, E. 

The air may be compressed in one or more cylinders through 
which it is passed in succession. When the compressor has 
one cylinder only, it is described as a one-stage or simple com- 
pressor; when two cylinders, as a compound or two-stage com- 
pressor; when three cylinders, as a three-stage compressor, etc. 

A section of a two-stage compressor with mechanically oper- 
ated inlet-valves, driven by a direct-connected steam-engine, is 

shown in Fig. 325. The air is first drawn into the large 

720 



§ 467.] 



A 1R- COMPRESSORS. 



J21 



cylinder, C, compressed to an intermediate pressure, after which 
it is delivered into the intercooler, B, thence to the small cylinder, 
C, when the compression is completed. 




Fig. 323.— Air-compressor Cylinder. 



To remove the heat generated during compression, the cylin- 
ders are usually jacketed with water, and in multiple-stage com- 
pressors the air is further reduced in temperature by passing 




Pig. 324.— The Ingersoll Air-compressor. 

through a vessel called an intercooler, which is located between 
the cylinders, and through which water is made to circulate in 
numerous small pipes. 



722 



EXPERIMENTAL ENGINEERING. 



f § 467 



w, 




(® © © @) 



cci 



fp 



<°) 



® 




468.] AIR-COMPRESSORS. 723 

Water-jacket cooling is very inefficient, and for that reason 
water is sometimes sprayed directly into the cylinder. This 
method of cooling is objectionable because of the moisture 
added to the air which may be converted into steam by the heat 
of compression. 

The clearance space in the air- compressor cylinders should 
be as small as possible, since this will be filled during the for- 
ward stroke with compressed air at full pressure, which will 
expand to atmospheric pressure on the return stroke of the pis- 
ton, and thus reduce the space available for the entering charge. 

Air-cooling is sometimes employed for removing the extra 
heat where the compressor cylinders are exposed to a draught 
of air, as, for instance, those used on locomotives for operating 
the air-brakes. 

Piston air- compressors are employed when high air pressures 
are required, but in some cases are used for low pressures, as, for 
instance, for blowing-engines for supplying the necessary air for 
steel furnaces. These are usually of the piston type, although 
the pressures rarely exceed 20 pounds per square inch. 

468. Rotary Blowers. — Rotary blowers consist of two 
revolving blades, or pistons, of such form as to drive the air for- 




FlG. 326. 



ward and maintain contact with the walls of the surrounding 
case and with each other so as to prevent leakage and a back- 
ward flow of the compressed air. A great variety of forms are 



724 



EXPERIMENTAL ENGINEERING. 



[§ 4^9. 



made, one of which is shown in Fig. 326. These blowers are suited 

for a pressure which does not exceed 20 pounds per square inch. 
469. Centrifugal Fans, or Blowers. — In the centrifugal 

fan, or blower, particles of air are moved radially by the centrifugal 

force set up by the blades of a revolving wheel, which produces 

a pressure head proportional to the 
square of the velocity of the circumfer- 
ence. Two types are in commmon use: 
(1) the propeller or disc form shown in 
Fig. 327, in which the current of air 
travels through the fan parallel to the 
axis, and (2) the blower type shown in 
Fig. 328, in which the air is received at 
the center of the wheel and discharged 

at the periphery into a casing or chamber from which it may 

be conveyed by pipes. 

The disc fan is not adapted to move air against any sensible 

pressure, and is generally employed for circulating large volumes 

of air. 




Fig. 327. 




Fig. 328. 



The blower type of fan is well adapted for pressures which 
do not exceed \ pound per square inch. By arranging blower 
fans in series, so that a fan working at low pressure supplies 
air to one working at higher pressure, the air can be compressed 
economically to a pressure of several pounds per square inch. 



§ 47°-] AIR-COMPRESSORS. J 2$ 

470. Measurement of Pressure and Velocity. — The 

pressure of compressed air is measured by a suitable type of 
pressure gauge or manometer as described in Chapter XI. When 
the pressure is high it is usually expressed in pounds per square 
inch or in atmospheres; when low it is usually expressed in 
fractions of a pound, or in ounces per square inch, or in inches 
of water or mercury. The relations of these units are shown 
in the table on page 336. 

The velocity of air may be measured directly by use of the 
anemometer described in Art. 233, or indirectly by use of the 
Pitot tube described in Arts. 222 and 223. The velocity may 
be computed from the formula 



v = c\/2ghr, 

in which v = velocity in feet per second of the air impinging 
against the Pitot orifice, h, the reading of the anemometer, r, 
the ratio of the density of the liquid in the manometer to that 
of the air, c, a coefficient to be found by calibration. 

When the air is at 32 F. and under a barometric pressure 
of 29.92 inches, and dry, one inch of water column will balance 
60.2 feet of air, consequently for that case r = 6o.2. 

The density of air increases directly with the absolute pres- 
sure, and inversely as the absolute temperature, it varies also 
with moisture so that corrections are required for pressure, tem- 
perature, and the amount of moisture. 

An extended use of the Pitot tube by the author has shown 
its accuracy for measurements of the velocity of air currents. 
The coefficient c will vary with the shape of the openings; with 
a tube of the form shown in Fig. 144, having an internal diam- 
eter of about \ inch and an opening at C of ■£% inch, c will be 
unity without sensible error. A straight tube with an opening 
in the side will give the same results as the bent nozzle shown 
in Fig. 144 and is much easier made. 

The Pitot tube,. shown in Fig. 146, may be arranged to give 
a value of c considerably higher than unity; for instance, if the 



7 26 EXPERIMENTAL ENGINEERING. [§ 470. 

end of the straight tube D is closed, and an opening made about 
J inch above the lower end at right angles to the directions of 
the current, the value of c may reach 1.4. With the opening 
in one tube pointing down-stream and in the other up-stream 
the value of c will equal about 1.25. 

In case the Pitot tube is used for determining the velocity 
in a pipe or channel, readings should be taken at regular intervals 
of depth. The mean velocity may be determined with little 
error by multiplying the velocity, which corresponds to each 
reading, by the area of section of which it forms the center, and 
dividing the sum of these products by the area of section. By 
constructing a velocity diagram, by laying off the velocities as 
abscissa to ordinates corresponding to depths, the mean velocity 
can also be obtained by dividing the area as obtained with a 
planimeter by this total depth or diameter. 

The velocity of air can be computed with accuracy by measur- 
ing the amount of heat required to warm it through an observed 
range of temperature, as follows: 

Let W represent the weight of air flowing in a given time, 
v its volume in cubic feet, d its weight per cubic foot or density, 
s its specific heat (which is constant and equals 0.238), V its 
velocity, F the area of section of moving air in square feet, t 
its initial temperature, t' its temperature after being heated, 
and H the heat of known amount in heat-units applied to warm 
the air from temperature / to t' . 

Since the heat absorbed by air is equal to the product of 
its weight, into its specific heat, into its rise of temperature, 

H~Ws(f-f)=vds(f-$i 

but since 

v = FV, 

H=FdsV{t f -f), 
from which the velocity 

v= H 



Fds{t'-t) 



§47iJ. 



A IE- COMPRESSORS. 



727 



A method of making the measurements as above is illus- 
trated in^ Fig. 329, in which the air enters the pipe or channel 
at A and is discharged at D. Means for heating the air, which 
may be either a steam or electric radiator, is to be supplied. If 
a steam radiator, the heat discharged is computed from measure- 
ments of the weight and temperature of the condensed steam, 
the heat entering from measurements of pressure, quality, and 
weight by methods already explained. The heat taken up by 
the air is the difference of that entering and discharged. If an 
electric heater is used, the electric energy disappearing is measured 
and reduced by computation to heat-units. The means for 
heating should be of such form as to heat the air uniformly, which 
can often be accomplished by adopting a suitable form of heater. 




Fig. 329. — Diagram of Method of Measuring Velocity of Air. 



The temperature of the entering and discharge air should 
be taken at sufficiently numerous points in the cross-section to 
make the average results accurate, and the thermometers should 
be protected from radiant heat. The average temperature should 
also be measured at the section where the velocity is to be com- 
puted. It may be desirable, in case extreme accuracy is required, 
to compute the weight of moisture in the air from observations 
with the dry- and wet-bulb thermometer. 

Direct-reading instruments, as the anemometer or Pitot tube, 
can be calibrated by comparison of numerous readings in a 
section with the velocity obtained as explained above. 

471. Effect of Clearance. — The effect of clearance in 
reducing the effective volume of the compressor cylinder may 



728 



EXPERIMENTAL ENGINEERING. 



[§ 472. 



be worked out from the relations of pressure, volume, and tem- 
perature, as given in equation (4) of Art. 462. 
It is readily shown from equation (4) that 



Vl 



(p 2 y /k 
= v AyJ ■ 



in which v 2 is the clearance volume in cubic feet, which is filled 
with air compressed to a pressure of p2 pounds per square foot 
at each stroke, v x is the volume after the same air has expanded 
to a pressure of pi pounds. 

The loss expressed in percentage of the cylinder displace- 
ment can be obtained by subtracting the volume at end of com- 
pression stroke from that at the beginning, which was occupied 
by the same mass of air, and dividing by the volume of piston 
displacement. If c = per cent, of clearance, and 100= piston 
displacement, then will 

c -4-) I/k 

percentage loss of volume =■ ■ =- — I 1 — ( ^ ] 1. 

472. Loss of Work Due to the Rise of Temperature. — 

The increase of temperature in adiabatic compression causes a loss 
of work. It can be computed by equation (6), Art. 462. The 
cooling of the air by the water-jacket is so slight that the actual 
compression curve, as shown on an indicator diagram, is usually 
very nearly coincident with the adiabatic curve. This causes 
a decided loss of work which is shown clearly by the diagram 
Fig. 330, which represents the work performed in compressing 
air in various ways. 

Thus the area of the diagram ABCFG represents the work 
of compressing a given volume of air isothermally, from o pressure 
by gauge (14.7 pounds absolute) to 120 pounds by gauge (134.7 
pounds absolute). The area of the diagram ADEFG represents 
in a similar manner the work done in compressing the same 
volume of air through the same pressures adiabatically. The 



§ 473-: 



A IR- COMPRESSORS. 



729 



difference in these areas shows the loss in work due to the rise 
of temperature during adiabatic compression. 

The diagram ADBHFG represents the compression of the 
same volume in a two-stage or compound compressor, with an 
intercooler. In this case the air is compressed adiabatically 



E H C 




Fig. 330. 



from A to D in the first cylinder, the excess of heat is removed 
by the intercooler, reducing the volume from D to B; it is then 
compressed adiabatically, B to H, in the second cylinder. The 
difference in area DBHE represents the saving in work by the 
two- stage or compound compressor as compared with the 
single compressor. 

473. Theory of the Centrifugal Blower.— In the opera- 
tion of the centrifugal blower the air is compressed so slightly 
that the change in pressure, volume, or temperature may be 
neglected in ordinary cases without producing sensible error. 

For this condition the volume Q recorded will be directlv 
proportional to the number of revolutions, n\ the pressure pro- 



73° EXPERIMENTAL ENGINEERING. [§ 474. 

duced, p, to the square of the number of revolutions; the work 
required, W , to the cube of the number of revolutions. 

A full discussion of this theory will be found in the author's 
work on " Heating and Ventilating of Buildings." 

The following formulas are nearly correct: 

Pressure produced, 



#3 =-7 U 2 [ I— £T ) , 

3600 \ FJ 



in which h 2 = pressure produced in inches of water, u= velocity 
of tips of blades, ft. per min., i?=area of outlet, i?i = area of 
inlet. 

Volume discharged, 

Q=KDdbn, 

in which Z) = outer diameter of fan- wheel, d = inner diameter 
of fan- wheel in feet, b= breadth of fan at tips in feet, n = num- 
ber of revolutions, K = sl constant for a given pressure. 

When db = 0.2$ D 2 , which is the usual proportion, K = o.6 
when h 2 = j, K = o.$ when h 3 = i, K = o.4 when h 2 = 2, approxi- 
mately. 

The work required. 

rOv 2 
W=^—=K'bdDH*. 

In which K f is a coefficient which decreases as the pressure 
increases. 

474. Test of Air-compressor. — The following tables 
suggest the observations that are needed for a complete test 
of an air- compressor. 

Air-compressor built by at 

Tested at < Date 190 

Cards integrated by Checked by 

Scale of springs. . . .Steam, left. . . .Steam, right.. .Air high press.. . Air low press. 



§ 474«] AIR-COMPRESSORS. 73 



DIMENSIONS. 

Steam-cylinders. 
Left. Right. 

Dia. in inches Dia. in inches 

Area in sq. in Area in sq. in 

Dia. piston rod in in Dia. piston rod in in. . . 

Area in sq. in Area in sq. in 

Length of stroke in feet Length of stroke in feet. 



Piston Displacement in Cubic Feet. 
Head Crank Head Crank. 



Volume in Clearances Per Cent. 

Head Crank Head Crank. 

Barometer inches Tempt, room 

Per cent, moisture in air 



Air-cylinders. 
High Pressure. Low Pressure. 

Dia. in inches Dia. in inches 

Area in sq. in Area in sq. in 



Diameter of Piston-rods in Inches. 
Head Crank Head Crank. 

Area of Piston-rods in Square Inches. 

Head Crank Head Crank. 

Length of stroke in ft Length of stroke in ft 



Piston Displacement in Cubic Feet. 
Head Crank Head Crank. 

Volume of Clearances per cent. 
Head Crank Head Crank. 



Revolutions : 

Continuous counter 

Per minute 

Boiler or steam-chest pressure. 

Reservoir pressure, air 

Nozzle pressure, air 



73 2 EXPERIMENTAL ENGINEERING. [§475- 

Temperatures: 

Entering low-pressure cylinder, air 

Leaving low-pressure cylinder, air 

Entering high-pressure cylinder, air 

Leaving high -pressure cylinder, air 

Nozzle, air 

Outside, air 

Calorimeter, steam 

Jacket -water: 

Entering cooler 

Leaving cooler or entering low-pressure cylinder 

Leaving low-pressure cylinder or entering high -pressure cylinder. •• • • 

Leaving high -pressure cylinder 

Weight of jacket- water, pounds 

Weight of condensed steam, pounds 

Heat absorbed by jacket-water: 

From cooler 

From low-pressure cylinder 

From high-pressure cylinder 

Total 

Quality of steam, per cent 

Mechanical efficiency, per cent 

Pounds of steam per I.H.P. per hour 

Cubic feet of air per piston displacement at standard conditions 

Cubic feet of air delivered as per nozzle at standard conditions 

Per cent slip 

Pounds of air compressed per hour, standard conditions 

Efficiency of compressor 

Volumetric efficiency 

Total efficiency of machine 

475. Test of Centrifugal Blower. — The following table 
suggests the quantities to be observed for a test of a centrifu- 
gal blower driven through a transmission dynomometer : 

Test of Centrifugal Blower. 



Kind Date 

Form of blades Discharge area 

Diameter of fan Temperature of room 

Width of fan Barometer 

Form of inlet Anemometer diameter 

Inlet area coefficient . . . . 

Formula Weight of air per cubic foot. 

Maker Moisture in air, per cent. . . 



Made by. 



§ 475-] 



A IR- COMPRESSORS. 



733 



No. of Run. 



Time begun 

Time ended 

Length of run 

Duration in minutes 

Tachometer 

R.P.M. of fan 

Air pressure per square inch, ounces 

Pressure head in water, inches 

Velocity " " " " 

Anemometer readings, inlet 

Temperature entering heating-box 

leaving 

Heat units absorbed 

Weights discharged per second 

Velocity of air, feet per second 

Cubic feet discharged per second 

Velocity of fan-blade tips, feet per second. 

Dynamometer reading 

Dynamometer horse-power 

Developed horse-power 

Cubic feet air per H.P. per second 

Efficiency, per cent 



CHAPTER XXV. 
MECHANICAL REFRIGERATION. 

476. Introduction. — Systems of mechanical refrigeration 
are extensively employed, either for maintaining a low tempera- 
ture or for the manufacture of ice, and some practical acquaint- 
ance with the processes successfully employed is of importance 
to the mechanical engineer. 

The refrigerating machine is a species of heat-engine, in 
which, by means of mechanical work, heat is transferred from 
one substance to another, the effect being to reduce or lower 
one temperature and increase the other. The ideal machine 
for this work is the reversible engine operating in a Carnot 
cycle in a reverse or backward direction from that of the steam- 
engine, the hot-air engine, and other heat-engines. 

The following illustrations will render this statement clear. 
Carnot' s reversible engine, when working as a heat-engine, 
takes from the source of heat a quantity, H, of which it changes 
a part, AW, into mechanical energy, and, as there are no losses, 
rejects the remainder, H ef to the refrigerator, b. We have for 
the efficiency, since H — H e = AW, 

_ AW H-H e T-T x 

E= ~ir = ~ir~ == ~T~' • ! W 

If the engine be run backward so as to describe its cycle in the 
reverse order, it takes heat from the refrigerator, adds to it the 
heat equivalent of the work of the cycle, and delivers the same 
to the source of heat and thus becomes a refrigerating machine. 

734 



§477J MECHANICAL REFRIGERATION. 72$ 

Th- efficiency becomes for this case 

1 AW H-H e T-Tf W 

'vhich is called the " Thermodynamic Efficiency." 

In a heat-engine operating in a Carnot cycle the working 
substance is first compressed adiabatically, in which case its tem- 
perature rises; second, it is compressed isothermally, in which 
case the temperature remains constant, which requires that the 
heat generated be absorbed and removed; then it is allowed to 
expand, adiabatically and isothermally, until the working sub- 
stance is in its orginal condition. During the last operation 
heat must be supplied the working substance to maintain a con- 
stant temperature. 

The equations expressing the relations between pressure, 
volume, and temperature during compression and expansion of 
a perfect gas are given in Art. 462, and should be referred to 
in connection with the investigation of the refrigerating machine. 

477. Relation of Mechanical Work to Heat Transfer. — 
The cycle of heat exchanges for a refrigerating machine of any 
class can be written for one unit of weight as follows : 

Let H = the original heat of the working substance; H 1 =the 
heat at end of compression, were none removed by cooling or 
loss ; H 2 = the heat at end of compression after cooling ; H 3 = 
the heat at end of expansion, supposing none removed for cool- 
ing purposes ; K = the heat taken up by the cooling liquid during 
compression and condensation; ifi=the heat taken up by the 
substance during refrigeration; AW c = th.e mechanical work of 
compression; AW e = the mechanical work done during expansion. 
We have then the following equations, expressed in heat-units, 
supposing no radiation or cylinder losses to exist: 

During compression, H +AW C =H X \ . . . (1) 

Cooling or condensation, H 1 — K=H 2 ; . . . . (2) 

During expansion, H 2 —AW e =H 3 ; ... (3) 

Refrigeration, H^ + Ki^H. . . . . (4) 



736 EXPERIMENTAL ENGINEERING. [§ 478. 

In the above equations K x is the measure of the refrigerating 
value, since it is the heat absorbed at the lowest temperature, 
and by substituting in the above equations we find that 

K 1 =H-H 3 =H-H 2 +AW e =H-H 1 +K^AW e 

=H-H 1 -AW c + K+AW e = K-A(W-W e ). . (5) 

That is, the possible heat transfer or refrigeration in the 
perfect machine is equal to the heat carried off by the cool- 
ing and condensing water, K, diminished by the difference of 
the heat equivalent of the work done in compression and in 
expansion. 

By transposing in equation (5), 

A(W e -W,)=K-K x (6) 

That is, the mechanical work in the perfect refrigerating 
machine is equivalent to the heat removed by cooling and 
condensing less that transferred from refrigerator to source of 
heat. 

478. The Efficiency of the Refrigerating Machine. — It 
has previously been shown, by equation (5), that, supposing no 
losses in the machine, the heat, K x , received from the refrigera- 
tor, increased by the heat equivalent of the mechanical work 
(AW C — W e ), equals the heat discharged, K. That is, represent- 
ing the net mechanical work by AW, 

AW=A(W c -W e )=K-K 1 (7) 

If the heat carried off in the condensing water cannot be 
utilized, the highest possible efficiency of the system is the 
ratio of the refrigeration K x to the work A(W c — W e )) that is, 
the possible efficiency E becomes, for that case, 

77 K i _ Kl fQ\ 

* A(W-W C ) K-K x W 



§ 47 8 -] MECHANICAL REFRIGERATION. 7S7 

If W is expressed in foot-pounds, A =jj^; if W is expressed in 
horse-power, A =42.42. 

The actual refrigerating machine not being perfect, the 
mechanical work expended, AW, is less than the increase in 
the heat transferred, and we should have for the actual machine 

AW<K-K X ( 9 ) 

The amount of refrigeration or cold produced is the quantity 
Ki f since that is the heat taken from the colder body and trans- 
ferred to the hotter. The object of the refrigerating process 
is the removal of the heat K\ f so that this may be considered 
the useful work. The total energy supplied is the mechanical 
work of compression. The efficiency of the actual machine 
is the ratio of the useful work to the total energy expended, 
and consequently is 

h2 ~A{W c -W e ) = AW' ' * ' * V (lo) 

The thermodynamic efficiency of a refrigerating machine 
operating in a Carnot cycle, as given in equation (h) f is the abso- 
lute temperature (^ = 460 + ^), divided by the rise in temperature 
(T — Ti). The ratio of the actual efficiency to this quantity, often 
called the " Coefficient 0} performance" E 3 , is a valuable standard 
of comparison: 

3 AW I\ AW T-Ti ' * * {1I) 

The thermodynamic efficiency of an engine working in a 
Carnot cycle is less than one, hence that in the refrigerator cycle 
must in every case be correspondingly greater than one. It 
mv.°t reach its limit, as noted by discussion of equation (9), when 
T—Ti has the least value, or when this value approaches o, 
in which case the limiting value of the efficiency approaches 
infinitv. 



73 8 EXPERIMENTAL ENGINEERING. [§ 479. 

The expression asserts what is certainly true, that for a given 
expenditure of work the output or energy discharged is much 
greater than that put in, or, from such a standpoint, the machine 
has a greater efficiency than unity. (See test, page 747.) 

Considering the refrigerating machine as the heat-engine 
reversed, it is noted that in the heat-engine the amount discharged 
by the exhaust is very great. In the case of a refrigerating machine 
heat is received at the lower temperature; in other words, flows 
in at the exhaust-pipe, is increased by the mechanical equiva- 
lent of the work done, and the total is discharged at a higher 
temperature. 

There is no reason why K^ should not be many times greater 
than AW; in fact they stand in no closer relation in a theoretical 
way than the heat discharged in the exhaust does to that trans- 
formed into work in the steam-engine. 

479. Negative Heat Losses. — In the case of the steam- 
engine, heat is taken from the steam to warm up the cylinder 
and keep it warm, giving rise to> the loss known as cylinder con- 
densation; in addition, heat is radiated into the surrounding 
space. These losses reduce the working value of the steam 20 
to 50 per cent. In the refrigerating machine similar losses of an 
opposite and negative character exist. 

The effect of the negative heat losses would be as follows : In 
the compression the cylinder becomes heated, and this heat is only 
partially discharged to the condenser; the remainder keeps the 
cylinder warmer than it otherwise would have been even at the 
end of expansion. This heat in the cylinder walls warms and 
expands the entering gas as it flows in, and has the effect of 
reducing its capacity, being thus exactly opposed in character, 
but otherwise similar to the loss of heat which occurs with a 
heat-engine. During a great part of the revolution the tem- 
perature in the cylinder is below that of the room, in which case 
heat will flow from the surrounding room into the working 
cylinder. 

480. The Working Fluid. — The working fluids are 
usually selected among the fixed gases, or from liquids whose 



§480.] MECHANICAL REFRIGERATION. 739 

boiling-point is very low. The principal freezing machines 
use either air, ammonia, or carbon dioxide, but water-vapor 
or steam may be employed. The properties desirable in a vapor 
or gas to be used for refrigeration purposes are: 

First, latent heat of vaporization large, which will permit 
the use of a small amount of working substance, since the capacity 
of a given weight to transfer heat is proportional to this quantity. 

Second, freezing-point low; as the capacity to absorb heat 
is a function of difference of temperature, the lower the tem- 
perature at which a given substance will remain liquid, the 
greater the capacity for a given weight, and also the lower the 
temperature which can be attained. It is hardly necessary to 
mention that a solid body cannot be pumped, and that as soon 
as it solidifies it becomes useless for refrigeration. 

Third, considerable change in temperature for moderate 
increase of pressure. In addition, commercial considerations 
render it necessary that the liquid shall be reasonable in cost, 
and shall be one that will not attack or destroy the machinery used. 

Water Vapor. — A steam-engine, run backward or as a com- 
pressor, with steam as a working substance, would convey heat 
from a lower to a higher temperature at the expense of the net 
work of compression. • In this case, however, the lower limit 
of temperature could not be much less than that of the freezing- 
point of water. In any case, when expansion occurred, an 
amount of heat equivalent to the latent heat of liquefaction 
would be absorbed from the surrounding medium. 

While steam or vapor of water has a very high latent heat, 
it becomes solid at a comparatively high temperature (32 F.), 
and consequently is not well suited for use in a refrigerating 
machine. 

In a pressure below that of the atmosphere considerable 
vapor is given off, and practical ice-making machines have been 
built to work under such conditions. These machines are known 
as water-vapor vacuum machines. 

Air. — An air-compressor would transfer heat, as already 
explained, by the mechanical work of compression. 



74Q 



EXPERIMENTAL ENGINEERING 



[ § 480. 



Anhydrous Ammonia. — This material is produced as a waste 
product in various industries in an impure form, and it needs 
only to be purified and separated from water to fit it for refrig- 
eration purposes. 

The material exerts 1 o corrosive action on iron, and for this 
reason does not affect in any degree the ordinary machinery 
for conveying or compressing it. 

It will, however, attack brass or copper and must be kept 
from contact with these metals. 

Its important properties are given in the following table: 

At atmospheric pressure boiling-point is 2 8. 6° F. Weight 
at 32° F., combined with water, is 0.6364, or 39.73 pounds per 
cubic foot, or 5.3 pounds per gallon. Specific heat is 0.50836. 
Latent heat at 32 F. is about 560 B.T.U. 

The following table, giving the principal properties for each 
10 degrees of temperature on the Fahrenheit scale, is taken 
from Professor Wood's Thermodynamics. 

PROPERTIES OF SATURATED ANHYDROUS AMMONIA. 



Degrees 
F. 


Pressure 
Absolute 

per 
Sq. Inch. 


Total 
Latent 
Heat. 


External 
Latent 
Heat. 


Internal 
Latent 
Heat. 


Volume of 
1 Pound 
of Vapor 
Cu. Ft. 


Volume of 
1 Pound 

of Liquid 
Cu.Ft. 


Weight of 
1 Cu. Ft. 

in Pounds. 






r 


apw 


5 








-40 


IO.69 


579-67 


48.25 


531-42 


24.38 


0.0234 


0.041 1 


-3° 


14-13 


573 


69 


48 


85 


524 


84 


18.67 


0.0237 


0-0535 


— 20 


18.45 


567 


67 


49 


44 


5i8 


23 


14.48 


. 0240 


. 0690 


— 10 


23-77 


56i 


61 


5° 


05 


5" 


56 


11.36 


0.0243 


0.0880 





30-37 


555 


5 


5i 


3^ 


5°4 


12 


9.14 


0.0246 


0. 1094 


10 


38.55 


549 


4 


5 1 


13 


498 


22 


7.20 


O . 0249 


0.1381 


20 


47-95 


543 


J 5 


5 1 


65 


491 


50 


5-82 


O.0252 


0. 1721 


3° 


59-4i 


536 


92 


52 


02 


484 


90 


4-73 


0.0254 


0.2111 


40 


73.00 


53° 


63 


52 


42 


478 


21 


3.88 


0.0257 


0.2577 


5° 


88.96 


5 2 4 


3 


52 


82 


47i 


44 


3.21 


0.0260 


°-3"5 


60 


107.60 


5i7 


93 


53 


21 


464 


76 


2.67 


0.0265 


0-3745 


70 


129. 21 


5 11 


5 2 


53 


67 


457 


95 


2.24 


0.0268 


0.4664 


80 


154. 11 


5°4 


66 


53 


96 


45° 


75 


1.89 


O.0272 


0.5291 


90 


182.8 


498 


11 


54 


28 


443 


70 


1. 61 


0.0274 


0.62 1 1 


100 


215.14 


491 


5 


54-54 


437-35 


1.36 


O.0279 


o-735 6 



§ 48 1 .] ME CHA NIC A L REFRIGERA TION. 74 1 

481. The Air-refrigerating Machine. — In this case air 
is compressed by mechanical means, and the heat which is 
generated is removed by a water-jacket, so that the temperature 
after compression is approximately the same as at the beginning. 
It is then permitted to expand adiabatically against a resistance 
so as to perform mechanical work, and in so doing falls in tem- 
perature. It can afterward take up heat from' the surrounding 
bodies. It was experimentally demonstrated by Joule that the 
temperature of air remains constant if it expands without doing 
external work. 

For the air-refrigerating machine W e in equation (5), the 
mechanical work done during expansion, is considerable; for 
the ammonia machine it is usually small and often zero. The 
heat capacity of any gas which does not change its state is small, 
and is equal to the product of specific heat, into weight, into 
change of temperature. On the other hand, when vapors are 
employed which are converted into liquids during the process 
of compression and cooling, and then changed into vapors during 
expansion, the heat capacity of a given weight is increased because 
of its latent heat, which is always comparatively large. It becomes 
quite evident from the latter consideration alone that the air 
machine must for a given capacity be many times greater in size 
than the ammonia machine. 

Two of the more successful machines of this type are described 
as follows: The Windhausen machine, which was operated 
during the Vienna Exposition, had a capacity of 30 cwt. of ice 
per hour. In its construction it consisted of a single cylinder, 
each end of which was alternately a compressed-air engine and 
a pump for compressing the air. The compressed air was de- 
livered to a cooling vessel, and from thence to one end of the 
cylinder, being admitted by a valve motion, and acting in its 
expansion to move the piston and help to compress the air drawn 
in at the other end. The exhaust air after, being deprived of 
its heat by the work of expansion, was passed to the cooling 
vessels, and utilized in lowering the temperature of a quantity 
of brine, or directly discharged for refrigeration purposes. The 



742 



EXPERIMENTAL ENGINEERING. 



[§ 482, 



power required over and above that provided by the compressed 
air was supplied by an engine. 

The Bell- Coleman machine, which is extensively used on 
shipboard for refrigeration purposes, is constructed in much 
the same manner as the Windhausen, but the operations of 
compressing and expanding are performed in separate cylinders. 
The machine consists of three tandem cylinders, and three pis- 
tons fixed to a common piston-rod. One cylinder is the air- 
compressor, the other the air-engine, while a third is a steam- 
engine which supplies the excess of power needed to move the 
pistons. 

The amount of work required and the change of temperature 
produced in the expansion and compression of air have been 
discussed quite fully in Art. 462. 

482. The Ammonia Compressor. — A general outline 
of an ammonia compression system is shown in Fig. 331. It 



. . Water Supply 

AmmOniSl IlCondenssrC 




Compression 
Refrigerating 
Apparatus 
Three Parts 



MitiiwiiiniMiiii; 11 iiiiiiHiiuiiiirnrMriuiiiiiiiiiniiffiiiiiiuq 

'iJiiiBimiiwiwiHiii^^^iniiwiuiiuiiiJitifmttiiiiuLW.HiiniiiffiiEi 
griii«iiiiiinuuiiiN'iiriuiiiiiiiiii(inu:uiriiiiiinjiiiin!nrniiin!iiiiiiii;iiiiKiiii::i 



h a T 
Brine Tank or Congealer A. 




Fig. 



-Outline Drawing of Mechanical Compression System. 



consists of a compressor or pump, B, which draws the ammonia 
vapor from the brine-tank or congealer, A, compresses it, and 
then delivers it to the large condenser, C, where it is cooled by 
water and is liquefied. The liquid ammonia under pressure 
is then permitted to flow through the expansion-valve shown 



§ 482.] MECHANICAL REFRIGERA TION. 743 

between the condenser and the brine- tank. In passing through 
the expansion-valve and into the expansion-pipe shown in the 
brine-tank, the liquid ammonia is vaporized by expansion, and 
the heat required is taken up from the material surrounding 
the coil. 

The apparatus as shown consists of three parts: (1) the 
expansion-valve and coil, in which the liquid is vaporized, (2) the 
compressor, in which the vapor is compressed; and (3) the con- 
denser, in which the vapor is reduced to a liquid. If there were 
no other heat losses, it is evident that the heat given off in the 
condenser would equal that drawn from the medium surrounding 
the expansion-coils. 

In the apparatus illustrated the expansion-coils are shown 
surrounded by brine. In many cases the expansion coils are 
in contact with the air of the room which is to be lowered in tem- 
perature. In some instances the brine, after being cooled by the 
expansion of ammonia, is circulated to the places where a low 
temperature is required. 

The compression cylinder for the ammonia refrigeration 
machine should be made with as small a clearance as possible, 
for the reasons which have already been given in the discussion 
of the air-compressor. Fig. 332 shows an enlarged view of a 
single-acting ammonia-compression cylinder surrounded with a 
water-jacket for removing heat during compression. In some 
instances ammonia compressors have been provided with means 
for keeping the clearance spaces filled with oil. In such cases 
an oil-separator is employed between the compressor and the 
condenser, which is arranged to take the oil out of the ammonia 
pipes and return it to the compressor. 

Refrigerating machines are used for the cooling of buildings 
and also for the manufacture of ice. For the manufacture of 
ice a brine- tank is usually employed which is maintained at low 
temperature by the expansion of ammonia in coils inserted in 
the tank substantially as shown in Fig. 331. The ice is usually 
made by freezing distilled water in cans of the desired shape. 
In nearly all ice-plants of this character, apparatus is required 



744 



EXPERIMENTAL ENGINEERING. 



[§483. 



not only for the ammonia system but also for supplying and 
purifying the water. Fig. 333 shows a section of an ice-making 
plant with all the principal parts named. The ' operation of 
the plant can be understood from a study of the drawing. 




Fig. 332. — Ammonia Compression Cylinder. 

Ice is also made by directly freezing water in contact with 
the expansion system. In such case the ice is frozen in large 
plates, and is usually removed by discharging hot ammonia liquid 
directly into the expansion system, which loosens it from the 
expansion plates. It is in such cases usually cut into small 
pieces by the use of jets of steam. 

483. Relations of Pressure and Volume. — In the 
compression of ammonia the relations of pressure, volume, and 
temperature are essentially as those given in equation in Art. 462. 
The compression is usually very nearly adiabatic, as indicated 
by the diagrams taken with an indicator. For the adiabatic 
curve of ammonia vapor, 



£ = 1.3. 



§ 483-: 



ME CHA NIC A L KEFRIGERA TION. 



745 




7 4 6 



EXPERIMENTAL ENGINEERING. 



[§ 483. 



In Fig. 334 is shown a series of adiabatic curves for different 
pressures and volumes drawn by Mr. R. L. Shipman, which wilL 
be found extremely useful in making a comparison of the com- 
pression line obtained on an indicator diagram with an adia- 
batic curve corresponding to the same pressure and volume. 













Hll'm\l\l!l\\\M\1\\\lMM\\\ 




lllllillllml\M\Mv\\\\\\\\ 




■MlllllHVMlMmiHHI ■■■■■■! ■■■■■■■■■■■■■■■■■■■■■■■■ 




■■niiminiimm\u\i\\\\«HHi ■■■■■■■■■■■■ ■■■■ 








I l \M\\\\\vM\\i 




\1\\\m\V\\\mu 




uISiumSBs 




iiimvSsSmS I 




iWmIimsl 




tt( SISSlK 




sifiisBsEawM 




SiBsQiEffioSwu 




irtJlrnSlHSS 




JrpMliSHI 




jrtitsfifisKSsSSv 




iQKQlSSKBfflSM 




nnEvasssMo^ 




SiSSMSM^H 




ftjirMcMssMSv- 


IT 


SLUqQSvMMMM 


ZD 


irivVasssMsssSv 


% 


3iGGGEGESSSS§S§5 + 


UJ 


IBrilAssssssSaSS^ 


cc 


IIMMYSV5SSSS|^ 








+XC\Xu$2ssSssSsSSs 




u\\ A v\ v\\\v V\ AA\VaXX^\ 




: ii\ Avssvss^gggSgs^ 




st^oSvxsSsSssSsSsi^ 




_. T3^SV3SX5SS5SSSS||S^^ 




^xvHv5\$$S5S$§§§§s§a^ 




Sa_v$w5_^s§Ss§s§|§|I^ 




: X^\^$sosss§s^|s|||ll^^ 




35_^_S5$s5§s§^l5l^l§§t§^ 




^S\_;S^^s|_;§5^|5il§lPSI§^ 








x^^S^xxSSS^^^^^^^^SSs^^S^^^^s*. 




\ s ^v^n > \^\ n * VvN *^^^5^:§^^^5:^5^<^:§§^^=s»«. 




^^\ \\^^^\SVS^5i;^^^g;;^g5^ ^5 = ^. 




\\\^^^^^^^^.^i;^555-^ ; 5;g5gg$5$§§§^S§§5S^ 




^^N^V^^^vS^-^v^^^^^v^J^^^^^SS- 




^^N^^S^^^^^^ii^^^^Ss^sS^sSSssisIs 




^-^-i^-^^-^?^?^?^?^^^?^ =3S5=5 = =S| 


^ 


"""--^^-^^^^"-■^^^Sr^sS— := — = = = =1=5 _ = 




— ~ = =~=: — = =— = _i := =:= = = :_ = — 




———======= 


, 


_____ 



Fig. 334.- 



VOLUME OR LENGTH OF STROKE 
-Adiabatic Curves for Different Pressures and Volumes. 



The following table gives the result of a series of tests on 
ammonia compression machines, made by C. Linde of Munich, 
and are of interest as showing the amount and character of the 
various quantities described The table is copied from a paper 
read before the American Society of Mechanical Enigneers, at 
the Chicago meeting, 1893. The units were reduced to one) 



484] 



MECHANICAL REFRIGERA TION. 



747 



minute of time instead of one hour. It is noted that in every 
case AW is less than K — K\, and it should also be further noted 
that the smaller this difference the greater the economical per- 
formance of the machine. 



Number of Test. 



Temp, of brine: Inlet, deg. F. . . 
Temp, of brine: Outlet, deg. F. . 
Specific heat of brine per unit of 

volume 

Quantity of brine per hr., cu. ft. . . 
Cold produced, B.T.U. per min., 

Kx 

Temp, of cooling water: Inlet, 

degs. F 

Temp, of cooling water: Outlet 

degs. F 

Quan. of cooling water per hr. 

cu. ft 

Heat removed by condenser per 

minute, B.T.U., K 

Increase in heat, K—K\ 

I.H.P. in comp. cyl., W 

Heat equivalent of work, AW. 
I.H.P. in steam-engine cylinder. . 
Consumption of steam per hour, 

lbs 

Consumption of steam per min- 
ute, lbs 

Cold produced in B.T.U. per 

minute per I.H.P. in comp. cyl. 
Cold produced in B.T.U. per 

minute per I.H.P. in steam 

cylinder 

Cold produced in B.T.U. per 

minute per pound of steam. . . . 
Thermodvnamic efficiency (460 + 

f)+(t c -t)=E 1 

Actual efficiency Ki-t-AW=E 2 . . 
Ratio of actual to thermodynamic 

efficiency 

AW-(K-Ki) 

* Lbs. of ice melted per lb. of 

steam 

Lbs. of ice melted per lb. of coal. . 



43- 2 
37-° 

0.861 
1039.4 

57I5-I 

48.8 

66.7 

338-7 

6305-9 
590.8 
13.82 
586.2 
15.80 

3H-5 

5-i9 
413-5 

361.7 

1 100 

17.2 
9-75 

0.56 
-4.6 

7-5 2 
75-2 



28 
22 

o 
908 

4309 

49 

68 

260 

5° 2 3 

724 

14 

606 

16 

336 

5 

3°7 



9 

851 



267. 1 

785-6 

10.65 
7.26 

0.68 
-118. 1 

5.66 
56.6 



1 3 

8 

o 
615 

2781 

49 

67 

187 

3509 
728 

13 

587 
15 

306 

5 
200 



9 

7 

843 
4 

3 

1 



180.7 

543-9 

8.04 
4-73 

°-59 
-141. 2 

3-85 
38.5 



~°-3 
-5-9 

0-837 
915.0 

2024.5 

49.1 

67-3 
140.0 

2648.7 
624.2 

11.98 
508.2 
14.24 

278.8 

4-65 

169.0 

142 .2 
435-8 

6.2 

4-03 

0.667 
-116. o 

3-i 
31.0 



28 
23 

o 
800 



3671 

49 

93 

97 

45i8 

847 

19 

837 

21 

43° 

7 
185 

169 

512 

6 
4 

o 
— 10 



851 
9 



86 
3* 

637 

4 

64 

4 



* Latent heat of ice taken as 141 B.T.U. 



484. The Absorption System of Refrigeration. — This 
system was invented by M. Carre, and dispenses with the ammo- 



74 8 EXPERIMENTAL ENGINEERING. [§ 484. 

nia compressor. Instead of compressing the ammonia by pres- 
sure, water strongly impregnated with ammonia gas is heated 
by steam. The heat vaporizes the ammonia and, because of 
the low boiling temperature of the ammonia, causes as much 
pressure as required. The compressed ammonia is treated 
as in the other processes, that is, it is first passed through a con- 
denser and liquefied, thence to expansion-coils, where it takes 
up heat from the surrounding material. Instead of being pumped 
hack as in the first system, it is absorbed by water and the dilute 
liquid is pumped. 

Fig. 335 shows a view of an absorption system with all the 
principal parts named. It is worthy of a close study, as showing 
the economy practiced in the use of the heat employed. 

The strong ammonia liquid from the absorber is pumped 
through a heater, where it is surrounded by weak ammonia 
liquor which had been previously heated in the gene ator. It 
then flows, partially heated, to the analyzer, where it exposes 
a large surface to the heat. The principal part of the ammonia 
gas under pressure passes off above, the weak ammonia liquor 
falls to the bottom of the generator. The ammonia gas under 
the pressure due to. its temperature is received in the condensing 
coil. In this coil the pressure is maintained, but the tempera- 
ture is lowered by the use of condensing water, so that the ammo- 
nia gas is converted into liquid anhydrous ammonia. 

The anhydrous ammonia is used as in the other systems; it 
may be allowed to expand in a tank filled with brine, or it may 
be carried to the rooms where refrigeration is needed and then 
permitted to expand. In the figure the brine system is shown, 
the expansion taking place in the cooler, in which a circulation 
of brine is maintained by a pump. 

The weak ammonia from the generator, after parting with 
some of its heat in the heater, is brought in contact with the 
ammonia in a vessel called the absorber. The ammonia gas 
has a strong affinity for water, and is absorbed readily, convert- 
ing the weak ammonia liquor into strong ammonia liquor. This 
is pumped to the heater and completes the cycle. The exhaust 






484.] 



MECHANICAL REFRIGERA TION. 



749 




75° EXPERIMENTAL ENGINEERING. [§ 484. 

steam from the pumps is utilized in heating under ordinary 
conditions, so that all the heat wastes are carried off in the con- 
densing water and in the drip from the generator. 

When a low back pressure is wanted, such as is required 
in production of ice, this system succeeds well, and is somewhat 
more economical than the compression system. For purposes 
of refrigeration where a high back pressure is maintained the 
compression system is more economical in its operation. 

The following sheets indicate the observations which are 
necessary for a complete test of an ammonia refrigerating machine : 



. LOG A. 

Test of Refrigerating Machine built by Style 

Tested at .' Date 

Size of Ammonia Cylinder — Diam Stroke Scale of Ind. Spring 

Capacity of Expansion Valve .... Specific gravity of Brine .... Barometer 

Test made by 

No 

Time 

Speed-counter 

Revolutions per minute 

Temperature, room . . . . : 

Temperature, external air 

Condenser: 

Temperature, entering gas 

Temperature, injecting water 

Temperature, discharging water 

Weight water lbs 

Compression gauge " 

Expansion Coils: 

Temperature, entering gas Deg- F- 

Temperature, discharging gas " 

Suction gauge lbs 

Brine Tank: 

Temperature, entering brine. 

Temperature, discharging brine 

Meter reading 

Cubic feet, brine 

"Weight of brine, pounds 

Revolutions of expansion valve 

Temperature, liquid NH 3 , at expansion valve 



§ 4 8 4-] MECHANICAL REFRIGERATION. 7$ I 



LOG B. 



Test of Refrigerating Machine built by , 

Tested at Date 

Tested by 

Specific gravity of NH 3 Specific heat of NH 3 . 

Specific gravity of brine Specific heat of brine. 

Number 

Brine: 

Pounds, circulated 

Range, temperature 

B.T.U. discharge 

Condenser: 

Pounds, water 

Range, temperature 

B.T.U. discharge 

Gain B.T.U 

Compression cylinder: 

Absolute pressure admitted 

Absolute pressure discharged 

M.E.P 

D.H.P 

Work, B.T.U 

Ammonia: 

Pounds, circulated 

Heat of vaporizion, suction pressure 

Heat of vaporizion, condenser pressure 

Temperature due to pressure in refrigerating coils 

Absolute pressure in refrigerating coils 



SPECIFIC HEAT OF BRINE. 



1. 170 


1. 103 


1.072 


1.044 


1.023 


1. 012 


.805 


.863 


.895 


• 931 


.962 


.978 



Specific Gravity 1 . 187 

Specific Heat 0.791 



SPECIFIC HEAT CHLORIDE OF CALCIUM SOLUTION. 

Specific Gravity 1.0255 1.163 

Specific Heat 0.957 0.827 



752 



EXPERIMENTAL ENGINEERING. 



[§ 484. 



REPORT. 

Test of Refrigerating Machine built by ; 

Tested at Date Latent heat of ice 142.2 

Tested by 



No. 



I 
2 
3 
4 
5 
6 

.7 
8 

9 
10 
11 
12 
13 
14 
15 
16 

17 
18 

J 9 
20 
21 
22 

23 
24 

25 

26 

27 



Pounds of condensing water per hour 

Range of temperature of condensing water 

Pounds of brine per hour 

Range of temperature of brine 

Pounds of ammonia per hour 

Pounds of condensing water per £ound of NH 3 

Average temperature outlet of brine 

Average temperature outlet of cooling water 

Temperature of NH 3 entering brine tank 

Corresponding sensible heat liquid above 32 in B.T.U. . 

Total heat NH 3 gas B.T.U. at suction pressure 

Temperature of gas leaving brine tank 

Temperature of gas corresponding to suction pressure 

Superheating of gas in degrees Fahrenheit 

Cooling per pound of ammonia in B.T.U 

Temperature of gas entering condenser 

Heat carried off by condensing H 2 per hour B.T.U. . . 
Heat taken from brine per hour B.T.U. (Refrigeration) 

D.H.P. ammonia cylinder 

Foot-pounds of work per hour, no friction 

Heat equivalent of work per hour B.T.U 

Heat carried from brine per pound NH 3 circulated. . . . 

Heat carried off by cond. H 2 per pound NH 3 cir 

Heat gained by system per hour B.T.U 

Thermodynamic efficiency 

Actual efficiency 

Ratio actual to thermal efficiency 

Ice-melting capacity pounds 24 hours at 100 revolutions 



Sym 
bols. 



Formulae. 






t-t 3 
^2—qi + o.^i d x 

QT 
QiTtX Spe. ht. 



AW 



K-Ki 

t + 4.61 

t c -t 

Ki-i-AW 

Ei + E 






LIST OF TABLES. 



PAGE- 

I. U. S. Standard and Metric Measures • 754 

II. Numerical Constants 756 

III. Logarithms of Numbers 769 

IV. Logarithmic Functions op Angles 771 

V. Naturae Functions op Angles 777 

VI. Coefficients of Strength of Materials 781 

VII. Strength of Metals at Different Temperatures 782 

VIII. Important Properties of Familiar Substances 783 

IX. Coefficient of Friction 784 

X. Hyperbolic or Naperian Logarithms 784 

XI. Moisture Absorbed by Air 785 

XII. Relative Humidity of the Air 785 

XIII. Table for Reducing Beaume's Scale-reading to Specific 

Gravity 786 

XIV. Composition of Various Facts of the United States 787 

XV. Buel's Steam-tables 788 

XVI. Entropy of Water and Steam 794 

XVII. Discharge of Steam : Napier Formula 795 

XVIII. Water in Steam by Throttling Calorimeter 795 

Diagram for Determining Per Cent of Moisture in Steam. 796 

XIX. Factors of Evaporation 797 

XX. Wrought-iron Welded Pipes 798 

XXI. Weight of Water at Various Temperatures 799 

XXII. Horse-power per Pound Mean Pressure 800 

XXIII. Water Computation Table 801 

XXIV. Weirs with Perfect End Contraction 803 

XXV. Weirs without End Contraction 803 

XXVI. Electrical Horse-power Table 803 

XXVII. Horse-power of Shafting 804 

XXVIII. Horse-power of Belting , 804 

Sample-sheet of Paper 804. 

753 



754 



EXPERIMENTAL ENGINEERING. 



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U. S. STANDARD AND METRIC MEASURES. 



755 



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756 



EXPERIMENTAL ENGINEERING. 



II. 

NUMERICAL CONSTANTS. 



n 


ffir 


4 


.. 


«s 


Vn 


3 


l.o 


3.142 


0.7854 


1. 000 


1. 000 


I. OOOO 


I. OOOO 


I.I 


3.456 


0.9503 


1. 210 


1. 331 


I.0488 


I .0323 


1.2 


3- 770 


1.1310 


1.440 


I.728 


I.0955 


I.0627 


13 


4.084 


1-3273 


1.690 


2.197 


I . 1402 


I. O914 


1.4 


4.398 


1-5394 


1.960 


2.744 


I. 1832 


I.II87 


1.5 


4.712 


1.7672 


2.250 


3-375 


1.2247 


I . 1447 


1.6 


5.027 


2.0106 


2.560 


4.096 


I . 2649 


I. 1696 


1-7 


5.341 


2.2698 


2.890 


4.913 


I.3038 


I- 1935 


1.8 


5-655 


2-5447 


3.240 


5.832 


I. 3416 


I. 2164 


1.9 


5.969 


2.8353 


3-6io 


6.859 


1.3784 


I.2386 


2.0 


6.283 


3.1416 


4.000 


8.000 


I. 4142 


I.2599 


2.1 


6-597 


3.4636 


4.410 


9.261 


I. 4491 


I.2806 


2.2 


6.912 


3.8013 


4.840 


10.648 


I.4832 


I . 3006 


2-3 


7.226 


4-1543 


5.290 


12.167 


I. 5 166 


I.3200 


2.4 


7-540 


4-5239 


5.760 


13.824 


1.5492 


1.3389 


2.- 


7-854 


4.9087 


6.250 


15625 


1.5811 


1-3572 


2.6 


8.168 


5.3093 


6.760 


I7.576 


1. 6125 


1. 3751 


2.7 


8.482 


5-7256 


7.290 


19.683 


1.6432 


1.3925 


2.8 


8-797 


6.1575 


7.840 


21.952 


1.6733 


1.4095 


2.9 


9. in 


6.6052 


8.410 


24.389 


1 . 7029 


1.4260 


3.0 


9-425 


7.0686 


9.00 


27.000 


1. 7321 


1.4422 


3.1 


9-739 


7-5477 


9.61 


29.791 


1.7607 


1. 4581 


3.2 


10.053 


8.0425 


10.24 


32.768 


1.7889 


1-4736 


3.3 


10.367 


8.5530 


10.89 


35-937 


1. 8166 


1.4888 


3.4 


10.681 


9.0792 


11-56 


39-304 


1.8439 


1.5037 


3-5 


10.996 


9.6211 


12.25 


42.875 


1.8708 


r.5183 


3-6 


11. 310 


10.179 


12.96 


46.656 


1.8974 


1.5326 


3-7 


11.624 


10.752 


13.69 


50.653 


1.9235 


1 • 5467 


3-8 


11.938 


11. 341 


14.44 


54.872 


1.9494 


1 . 56O5 


3-9 


12.252 


11.946 


15.21 


59.3I9 


1.9748 


1 -5741 


4.0 


12.566 


12.566 


16.00 


64.000 


2.0000 


1.5874 


4-1 


12.881 


13.203 


16.81 


68.921 


2.0249 


1 . 6005 


4.2 


13-195 


13-854 


17.64 


74.088 


2.0494 


1. 6134 


4-3 


13 509 


14-522 


18.49 


79-507 


2.0736 


1. 6261 


4-4 


13.823 


15-205 


19.36 


85.184 


2.0976 


1.6386 


4-5 , 


14 137 ! 


15 90* ' 


20.25 


91.125 


2.1213 


1. 6510 


4.6 


14-451 
14.765 


16.619 1 
17.349 1 


21.16 


97-336 


2 . 1448 


1. 6631 


.4.7 


22.09 


103.823 


2.I680 


1 6751 



NUMERICAL CONSTANTS. 



7S7 







Constants — Continued. 






n 


nit 


4 


»» 


»» 


Vn 


s 


4-8 


15.080 


18.096 


23.04 


110.592 


2 . I9O9 


1.6869 


4-9 


15.394 


18.857 


24.01 


117.649 


2.2136 


1.6985 


5-o 


I5.708 


19-635 


25.00 


125.000 


2.2361 


I. 7100 


5.1 


I6.022 


20.428 


26.0I 


132.651 


2.2583 


1. 7213 


5.2 


16.336 


21.237 


27.04 


140.608 


2.2804 


1.7325 


5.3 


16.650 


22.062 


28.09 


148.877 


2.3022 


1 • 7435 


5-4 


16.965 


22.902 


29.16 


157.464 


2.3238 


1-7544 


5-5 


17.279 


23.758 


30.25 


166.375 


2.3452 


1.7652 


5.6 


17.593 


24.630 


3I-36 


175-616 


2.3664 


1.7758 


5.7 


17.907 


25.518 


32.49 


185.193 


2.3875 


1.7863 


5.8 


I8.22I 


26.421 


33-64 


195. 112 


2.4083 


1.7967 


5-9 


18.535 


27.340 


34.81 


205.379 


2.429O 


1 . 8070 


6.0 


18.850 


28.274 


36.OO 


216.000 


2-4495 


1.8171 


6.1 


19.164 


29.225 


37-21 


226.981 


2.4698 


1.8272 


6.2 


19.478 


30.191 


38.44 


238.328 


2 . 49OO 


1. 8371 


6.3 


19.792 


31.173 


39-69 


250.047 


2.5IOO 


1.8469 


6.4 


20.106 


32.170 


4O.96 


262.144 


2.5298 


1.8566 


6.5 


20.420 


33-183 


42.25 


274.625 


2-5495 


1.8663 


6.6 


20.735 


34.212 


43-56 


287.496 


2.569I 


1.8758 


6.7 


21.049 


35.257 


44.89 


300.763 


2.5884 


1.8852 


6.8 


21.363 


36.317 


46.24 


3I4-432 


2.6077 


1.8945 


6.9 


21.677 


37-393 


47.61 


328.509 


2.6268 


1.9038 


7.0 


21.991 


38.485 


49.00 


343 . 000 


2.6458 


1. 9129 


7.1 


22.305 


39-592 


50.4I 


357-9" 


2 . 6646 


1.9220 


7.2 


22.619 


40.715 


51.84 


373-248 


2.6833 


1. 93io 


7-3 


22.934 


41.854 


53-29 


389-017 


2.7019 


1-9399 


7-4 


23.248 


43.008 


54-76 


405.224 


2.7203 


1.9487 


7-5 


23.562 


44.179 


56.25 


421.875 


2.7386 


1-9574 


7.6 


23.876 


45.365 


57.76 


438.976 


2.7568 


1. 9661 


7.7 


24.190 


46.566 


59-29 


456.533 


2-7749 


1-9747 


7-8 


24.504 


47.784 


60.84 


474-552 


2.7929 


1.9832 


7.9 


24.819 


49.017 


62.41 


493-039 


2.8107 


1. 9916 


8.0 


25.133 


50.266 


64.00 


512.000 


2.8284 


2.0000 


8.1 


25.447 


51.530 


65.61 


531.441 


2.846I 


2.0083 


8.2 


25.761 


52.810 


67.24 


551.468 


2.8636 


2.0165 


8-3 


26.075 


54.106 


68.89 


571.787 


2.88IO 


2.0247 


8.4 


26.389 


55-418 


70.56 


592.704 


2.8983 


2.0328 


8.5 


26 . 704 


56.745 


72.25 


614.125 


2.9155 


2 . 0408 


8.6 


27.018 


58.088 


73.96 


636.056 


2.9326 


2.0488 


8.7 


27.332 


59-447 


75.69 


658.503 


2.9496 


2.0567 


8.8 


27.646 


66.821 


77-44 


681.473 


2.9665 


2 . 0646 


8.9 


27.960 


62.211 


79.21 


704.969 


2.9833 


2.0724 



758 



EXPERIMENTAL ENGINEERING. 
Constants — Continued. 



ft 


nw 


4 


«» 


«3 


^ 


h 


9 o 


28.274 


63.617 


81.00 


729.OOO 


3.0000 


2.0801 


9.1 


28.588 


65.039 


82.81 


753.571 


3.OI66 


2.0878 


9.2 


28.903 


66.476 


84.64 


778.688 


3 0332 


2.0954 


9-3 


29.217 


67.929 


86.49 


804.357 


3-0496 


2 . 1029 


9.4 


29-531 


69.398 


88.36 


83O.584 


3.0659 


2.1105 


9-5 


29.845 


70.882 


90.25 


857.375 


3.0822 


2.1179 


9.6 


30.I59 


72.382 


92.16 


884.736 


3.0984 


2.1253 


97 


30.473 


73.898 


94.09 


912.673 


3-II45 


2.1327 


9.8 


30.788 


75.430 


96.04 


941 . 192 


3.1305 


2.1400 


9.9 


31.102 


76.977 


98.01 


970.299 


3.1464 


2.1472 


10. 


3I.4r6 


78.540 


100.00 


IOOO.OOO 


3.1623 


2.1544 


10. 1 


3I-730 


80.II9 


102.01 


1030 . 30I 


3.1780 


2.1616 


10.2 


32.044 


81.713 


104.04 


I06l.208 


3-1937 


2.1687 


10.3 


32.358 


83.323 


106 . 09 


1092.727 


3.2094 


2.1757 


10.4 


32.673 


84.949 


108.16 


II24.863 


3.2249 


2.1828 


10.5 


32.987 


86.590 


110.25 


II57.625 


3.2404 


2.1897 


10.6 


33.30I 


88.247 


112.36 


II9I.OI6 


3-2558 


2.1967 


10.7 


33-615 


89.920 


114.49 


1225.043 


32711 


2 . 2036 


10.8 


33.929 


91 .609 


116.64 


1259.712 


3-2863 


2.2104 


10.9 


34.243 


93-313 


118. 81 


1295.029 


3-3015 


2.2172 


11. 


34-558 


95.033 


121.00 


I33I.OOO 


3-3166 


2.2239 


II. 1 


34.872 


96 . 769 


123.21 


I367.63I 


3-3317 


2.2307 


11. 2 


35-186 


98.520 


125.44 


I4O4.928 


3.3466 


2.2374 


"•3 


35-500 


IOO.29 


127.69 


1442.897 


3-3615 


2.2441 


11. 4 


35-814 


I02.07 


129.96 


I48I.544 


3-3764 


2.2506 


11. 5 


36.128 


IO3.87 


132.25 


1520.875 


33912 


2.2572 


II. 6 


36.442 


IO5.68 


134-56 


I560.896 


3-4059 


2.2637 


11. 7 


36.757 


I07.5I 


136.89 


l60I.6l3 


3.4205 


2.2702 


11. 8 


37-071 


IO9.36 


139.24 


I643.O32 


3-4351 


2.2766 


11. 9 


37-385 


III. 22 


141. 61 


I685.I59 


3.4496 


2.2831 


12.0 


37.699 


113-10 


144.00 


I728.OOO 


3.4641 


2.2894 


12. 1 


38.013 


114.99 


146.41 


I77I.56I 


3.4785 


2.2957 


12.2 


38.327 


116.90 


148.84 


I815.848 


3.4928 


2.3021 


12.3 


38.642 


118.82 


151.29 


I860.867 


3 5071 


2 . 3084 


12.4 


38.956 


120.76 


153.76 


I906.624 


3.5214 


2.3146 


12.5 


39-270 


122.72 


156.25 


1953.125 


3-5355 


2 . 3208 


12.6 


39.584 


124.69 


158.76 


20OO.376 


3-5496 


2.3270 


12.7 


39-898 


126.68 


161.29 


2048.383 


3-5637 


2.3331 


12.8 


40.212 


128.68 


163.84 


2097.152 


3.5777 


2.3392 


12.9 


40.527 


130.70 


166.41 


2146.689 


3-59 J 7 


2.3453 


13.0 


40.841 


132.73 


169.00 


2I97.OOO 


36056 


2.3513 


13. 1 


41.155 


134-78 


171. 61 


2248.O9I 


3.6194 


2.3573 


13.2 


41.469 


136.85 


174.24 


2299.968 


3-6332 


2 . 3633 



NUMERICAL CONSTANTS. 
Constants — Continued. 



759 



n 


nit 


4 


»* 


»3 


Vn 


s 


13-3 


41.783 


138.93 


176.89 


2352.637 


3.6469 


2.3693 


13.4 


42.097 


I4I.03 


I79-56 


2406.104 


3.6606 


2.3752 


13-5 


42.412 


143-14 


182.25 


2460.375 


3.6742 


2.3811 


13.6 


42.726 


145-27 


184.96 


2515.456 


3.6878 


2.3870 


13-7 


43-040 


I47.4I 


187.69 


2571.353 


3.7013 


2.3928 


13.8 


43-354 


149.57 


190.44 


2628.072 


3.7148 


2.3986 


13-9 


43.668 


I5L75 


193.21 


2685.619 


3.7283 


2.4044 


14.0 


43.982 


153-94 


196.00 


2744.000 


3.7417 


2.4101 


14. 1 


44.296 


156.15 


198.81 


2803.221 


3.7550 


2.4159 


14.2 


44.611 


158.37 


201 . 64 


2863.288 


3.7683 


2.4216 


14.3 


44-925 


160.61 


204.49 


2924.207 


3-7^15 


2.4272 


14.4 


45-239 


162.86 


207.36 


2985.984 


3-7947 


2.4329 


14.5 


45-553 


165.13 


210.25 


3048.625 


3.8079 


2.4385 


14.6 


45.867 


167.42 


213. 16 


3112.136 


3.8210 


2.4441 


14.7 


46.181 


169.72 


216.09 


3176.523 


3.834I 


2.4497 


14.8 


46.49° 


172.03 


219.04 


3241 . 792 


3.847I 


2.4552 


14.9 


46.810 


174-37 


222.01 


3307 -949 


3 . 8600 


2.4607 


15.0 


47-124 


176.72 


225.00 


3375.000 


3.8730 


2.4662 


15. 1 


47-438 


179.08 


228.01 


3442.951 


3-8859 


2.4717 


15.2 


47.752 


181.46 


231.04 


3511-808 


3.8987 


2.4772 


15.3 


48.066 


183.85 


234-09 


3581.577 


3.9 JI 5 


2.4825 


15-4 


48.381 


186.27 


237.16 


3652.264 


3.9243 


2.4879 


.15.5 


48.695 


188.69 


240.25 


3723.875 


3.9370 


2.4933 


15.6 


49.009 


191. 13 


243.36 


3796.416 


3-9497 


2.4986 


X5-7 


49-323 


193-59 


246.49 


3869.893 


3.9623 


2 . 5039 


15-8 


49,637 


196.07 


249 . 64 


3944.312 


3-9749 


2 . 5092 


1 15.9 


49-951 


198.56 


252.81 


4019.679 


3.9875 


2.5146 


16.0 


50.265 


201.06 


256.00 


4096.000 


4.0000 


2.5198 


16. 1 


50.580 


203.58 


259-21 


4173.281 


4.0125 


2.5251 


16.2 


50.894 


206.12 


262.44 


4251.528 


4.0249 


2.5303 


16.3 


51.208 


208.67 


265.69 


4330.747 


4-0373 


2.5355 


16.4 


51.522 


211.24 


268.96 


4410.944 


4.0497 


2.5406 


16.5 


51-836 


213.83 


272.25 


4492.125 


4.0620 


2.5458 


16.6 


52.150 


216.42 


275.56 


4574.296 


4-0743 


2.5509 


16.7 


52.465 


219.04 


278.89 


4657.463 


4.0866 


2.5561 


16.8 


52.779 


221.67 


282.24 


4741.632 


4.0988 


2.5612 


16.9 


53-093 


224.32 


285.61 


4826.809 


4.1110 


2 . 5663 


17.0 


53-407 


226 98 


289.00 


4913.000 


4.1231 


2.5713 


17. 1 


53-721 


229.66 


292.41 


5000.211 


4.I352 


2.5763 


17.2 


54-035 


132.35 


295.84 


5088.448 


4-1473 


2.5813 


i7o 


54-350 


235.06 


299 . 29 


5I77.7I7 


4-1593 


2.5863 


17.4 


54-064 


23^.79 


302 . 76 


5268.024 


4.I7I3 


2.5913 



y6o 



EXPERIMENTAL ENGINEERING. 
Constants— Continued. 



n 


nit 


4 


*» 


«» 


lTn 


h 


17-5 


54.978 


240.53 


306.25 


5359-375 


4-1833 


2.5963 


17.6 


55.292 


243.29 


3O9.76 


545L776 


4.1952 


2.6012 


17.7 


55.606 


246 . 06 


313-29 


5545.233 


4.2071 


2.6061 


17-8 


55.920 


248.85 


316.84 


5639.752 


4:2190 


2.6109 


17.9 


56.235 


251.65 


320.41 


5735-339 


4.2308 


2.6158 


18.0 


56.549 


254-47 


324.00 


5832.000 


4.2426 


2 . 6207 


18. 1 


56.863 


257.30 


327.61 


5929.741 


4.2544 


2.6256 


18.2 


57.177 


26o.l6 


33L24 


6028.568 


4.2661 


2 • 6304 


18.3 


57-491 


263.02 


334.89 


6128.487 


4.2778 


2.6352 


I8.4 


57.805 


265.9O 


338.56 


6229.504 


4-2895 


2.64OI 


18.5 


58.II9 


268.80 


342.25 


6331.625 


4.3012 


2 . 6448 


18.6 


58.434 


271.72 


345.96 


6434.856 


4-3I2S 


2.6495 


18.7 


58.748 


274.65 


349.69 


6539.203 


4-3243 


2.6543 


18.8 


59.062 


277.59 


353-44 


6644.672 


4-3359 


2.6590 


18.9 


59-376 


280.55 


357-21 


6751.269 


4-3474 


2.6637 


I9.0 


59-690 


283.53 


36I.OO 


6859.000 


4.3589 


2.6684 


19. 1 


60.004 


286.52 


364.8I 


6967.871 


4.3703 


2.673I 


19.2 


60.319 


2S9.53 


368.64 


7077.888 


4.3818 


2.6777 


19-3 


60.633 


292.55 


372.49 


7189.057 


4.3932 


2.6824 


19-4 


60.947 


295.59 


376.36 


7301.384 


4.4045 


2.6869 


19- 5 


61.261 


298.65 


380.25 


7414.875 


4-4159 


2.6916 


19.6 


61.575 


301.72 


384.16 


7529-536 


4.4272 


2.6962 


19-7 


61.889 


304.81 


388.O9 


7645.373 


4.4385 


2.7008 


19.8 


62 . 204 


307.91 


392.04 


7762.392 


4.4497 


2.7053 


19-9 


62.518 


3".03 


396.01 


7880.599 


4 . 4609 


2.7098 . 


20.0 


62.832 


3I4.I6 


400.00 


8000.000 


4.4721 


2.7144 


20.1 


63.146 


317.31 


4O4.OI 


8120.601 


4.4833 


2.7189 


20.2 


63.460 


320.47 


4O8 . 04 


8242.408 


4-4944 


2.7234 


20.3 


63.774 


323.66 


4I2.09 


8365.427 


4-5055 


2.7279 


20.4 


64.088 


326 85 


4l6.l6 


8489.664 


4.5!66 


2.7324 


20.5 


64.403 


330.06 


420.25 


8615.125 


4.5277 


2.7368 


20.6 


64.717 


333-29 


424.36 


8741.816 


4.5387 


2; 7413 


20.7 


65.031 


336.54 


428.49 


8869.743 


4-5497 


2-7457 


20.8 


65-345 


339-8o 


432.64 


8989.912 


4-5607 


2.7502 


20.9 


O5.659 


343.07 


436.81 


9129.329 


4.5716 


2-7545 


21.0 


65.973 


346.36 


44I.OO 


9261.000 


4.5826 


2.7589 


21. 1 


66.288 


349-67 


445.21 


9393-931 


4-5935 


2.7633 


21.2 


66.602 


352.99 


449.44 


9528.128 


4.6043 


2 . 7676 


21.3 


66.916 


356.33 


453-69 


9663.597 


4.6152 


2.772O 


21.4 


67.230 


359-68 


457-96 


9800.344 


4.6260 


2.7763 


21.5 


67.544 


363-05 


462.25 


9938.375 


4.6368 


2.7806 


21 ..6 


67.858 


366.44 


466.56 


10077.696 


4.6476 


2.7849 


21.7 


68.173 


369.84 


470.89 


10218.313 


4.6583 


2.7893 






NUMERICAL CONSTANTS. 
Constants— Continued. 



761 



It 


nit 


4 


«a 


«3 


V„ 


3 


21.8 


68.487 


373-25 


475.24 


10360.232 


4.6690 


2.7935 


21.9 


68 . 801 


376.69 


479.61 


IO5O3.459 


4.6797 


2.7978 


22.0 


69.115 


380.13 


484.00 


IO648.OOO 


4 . 6904 


2 . 8021 


22.1 


69.429 


383-60 


488.41 


IO793.861 


4.7011 


2 . 8063 


22.2 


69-743 


387.08 


492.84 


IO94I.O48 


4-7II7 


2.8105 


22.3 


70.058 


39°- 57 


497.29 


IIO89.567 


4.7223 


2.8147 


22.4 


70.372 


394.08 


501.76 


11239.424 


4.7329 


2.8189 


22.5 


70.686 


397.61 


506.25 


II39O.625 


4-7434 


2.8231 


22.6 


71.000 


401.15 


510.76 


II543-I76 


4-7539 


2.8273 


22.7 


7I-3I4 


404 .71 


5I5.29 


II697.083 


4.7644 


2.8314 


22.8 


71.268 


408.28 


519.84 


11852.352 


4-7749 


2.8356 


22.9 


71.942 


411.87 


524-41 


I2OO8.989 


4-7854 


2.8397 


23.O 


72.257 


4I5-48 


529.00 


I2I67.O0O 


4.7958 


2.8438 


23.1 


72.571 


419.10 


533-6i 


12326.391 


4.8062 


2.8479 


23.2 


72.885 


422.73 


538.24 


I2487.168 


4.8166 


2.8521 


23-3 


73-199 


426.39 


542.89 


12649.337 


4.8270 


2.8562 


23-4 


73.513 


430.05 


547-56 


I28I2.904 


4-8373 


2 . 8603 


23.5 


73.827 


433-74 


552.25 


12977.875 


4.8477 


2.8643 


23.6 


74.142 


437-44 


556.96 


13144.256 


4.8580 


2.8684 


23-7 


74.456 


441.15 


561.69 


13312.053 


4.8683 


2.8724 


23.8 


74.770 


444.88 


566.44 


13481.272 


4.8785 


2.8765 


23-9 


75.084 


448.63 


571.21 


I365I.9I9 


4.8888 


2.8805 


24.0 


75-398 


452.39 


57600 


I3824.OOO 


4.8990 


2.8845 


24.1 


75-712 


456.17 


580.81 


13997.521 


4.9092 


2.8885 


24.2 


76.027 


459.96 


585.64 


I4172.488 


4-9193 


2.8925 


24.3 


76.341 


463.77 


590.49 


I4348.9O7 


4.9295 


2.8965 


24.4 


76.655 


467.60 


595-36 


14526.784 


4.9396 


2 . 9004 


24.5 


76.969 


471.44 


600.25 


I4706.I25 


4.9497 


2.9044 


24.6 


77.283 


475.29 


605.16 


I4886.936 


4.9598 


2 . 9083 


24.7 


77-597 


479.16 


610.09 


I5O69.223 


4-9699 


2.9123 


24.8 


77.911 


483-05 


615.04 


15252.992 


4.9799 


2.9162 


24-9 


78.226 


486.96 


620.01 


15438.249 


4.9899 


2.9201 


25.0 


78.540 


490.87 


625.00 


I5625.OOO 


5 . 0000 


2.9241 


25.1 


78.854 


494.81 


630.01 


I58I3-25I 


5-0099 


2.9279 


25.2 


79.168 


498.76 


635.04 


I60O3.OO8 


5.0199 


2.9318 


25-3 


79-482 


502.73 


640.09 


I6194.277 


5.0299 


2.9356 


25 4 


79.796 


506.71 


645.16 


I6387.064 


5-0398 


2-9395 


25-5 


80. in 


510.71 


650.25 


I658I.375 


5-0497 


2.9434 


25.6 


80.425 


5I4-72 


655-36 


16777.216 


5.0596 


2.9472 


25-7 


80.739 


518.75- 


660.49 


I6974.593 


5.0695 


2.9510 


25.8 


81.053 


522.79 


665 . 64 


I7I73.5I2 


5-0793 


2.9549 


25-9 


81.367 


526.85 


670.81 


17373-979 


5.0892 


2.9586 



762 



EXPERIMENTAL ENGINEERING. 
Constants — Continued. 



n 


mt 


A 


«» 


« 9 


v« 


3 


26.0 


81.681 


530.93 


676.00 


17576.000 


5.O99O 


2 . 9624 


26.1 


81.996 


535.02 


681.21 


I7779-58I 


5 . 1088 


2.9662 


26.2 


82.310 


539-13 


686.44 


17984.728 


5.H85 


2.9701 


26.3 


82.624 


543.25 


691.69 


18191.447 


5.1283 


2.9738 


26.4 


82.938 


547-39 


696.96 


18399.744 


5.1380 


2.9776 


26.5 


83.252 


551-55 


702 . 25 


18609.625 


5.1478 


2.9814 


26.6 


83.566 


555-72 


707.56 


18821.096 


5.1575 


2.985I 


26.7 


83.881 


559-90 


712.89 


19034.163 


5.1672 


2.9888 


26.8 


84.195 


564.10 


718.24 


19248.832 


r.1768 


2.9926 


26.9 


84.509 


568.32 


723.61 


19465 . 109 


5.1865 


2.9963 


27.O 


84.823 


572.56 


729.00 


19683.000 


5 . 1962 


3.0000 


27.I 


85-137 


576.80 


734.41 


19902. 511 


5.2057 


3.0037 


27.2 


85.45I 


581.07 


739-84 


20123.648 


5-2153 


3.O074 


273 


85.765 


585.35 


745.29 


20346.417 


5.2249 


3-oni 


27.4 


86.080 


589-65 


750.76 


20570.824 


5.2345 


3-OI47 


27.5 


86.394 


59396 


756.25 


20796.875 


5.2440 


3.0184 


27.6 


86.708 


598.29 


761.76 


21024.576 


5.2535 


3.0221 


27.7 


87.022 


602 . 63 


767.29 


21253.933 


5.2630 


3.0257 


27.8 


87.336 


606.99 


772.84 


21484.952 


5-2725 


3.0293 


27.9 


87.650 


611.36 


778.41 


21717.639 


5.2820 


3-0330 


28.0 


87.965 


615-75 


784.00 


21952.000 


5-29I5 


3-0366 


28.1 


88.279 


620.16 


789.61 


22188.041 


5.3009 


3.0402 


28.2 


88.593 


624.58 


795-24 


2 242 L. 768 


5-3I03 


3.0438 


28.3 


88.907 


629.02 


800.89 


22 65. 187 


5-3197 


3-0474 


28.4 


89.221 


633-47 


806.56 


22906.304 


5-329I 


3.0510 


28.5 


89-535 


637.94 


812.25 


23149.125 


5.3385 


3.0546 


28.6 


89.850 


642.42 


817.96 


23393-656 


5.3478 


3.0581 


28.7 


90. 164 


646.93 


823.69 


23639.903 


5.3572 


3.0617 


28.8 


90.478 


651.44 


829.44 


23887.872 


5.3665 


3.0652 


28.9 


90.792 


655.97 


835-21 


24137.569 


5-3758 


3.0688 


29.0 


91 . 106* 


660.52 


841.00 


24389.OOO 


5-3852 


3.0723 


29.1 


91.420 


665.08 


846.81 


24642.I7I 


5-3944 


3.0758 


29.2 


91-735 


669.66 


852.64 


24897.088 


5.4037 


3- 0794 


29.3 


92.049 


674.26 


858.49 


25153.757 


5.4129 


3.0829 


29.4 


92.363 


678.87 


864.36 


25412.184 


5.4221 


3.0864 


29 5 


92.677 


683.49 


870.25 


25672.375 


54313 


3.0899 


29.6 


92.991 


688.13 


876.16 


25934.336 


5-4405 


3.0934 


29.7 


93.305 


692.79 


882.09 


26198.073 


5-4497 


3 . 0968 


29.8 


93.619 


697.47 


888.04 


26463.592 


5.4589 


3.1003 


29.9 


93-934 


702.15 


894.01 


26730.899 


5.4680 


3-1038 


30.0 


94.248 


706.86 


900.00 


27OOO.OOO 


5.4772 


3.1072 


30.1 


94-562 


711.58* 


906.01 


2727O.9OI 


5.4863 


3.1107 


30.2 


94.876 


716.32 


912.04 


27543-608 


5-4954 


3.1141 



NUMERICAL CONSTANTS. 
Constants — Continued. 



763 



n 


HIT 


4 


«» 


«* 


Vn 


3 


30.3 


95.190 


721.07 


918.09 


278l8.I27 


5 • 5045 


3-II76 


30-4 


95 • 505 


725-83 


924.16 


28094.464 


5.5I36 


3.1210 


30- 5 


95.819 


730.62 


930.25 


28372.625 


5.5226 


3.1244 


30.6 


96.133 


735-42 


936.36 


28652.616 


5.5317 


3.1278 


30.7 


96.447 


740.23 


942.49 


28934.443 


5.5407 


3.1312 


30.8 


96.761 


745.06 


948 . 64 


29218. 112 


5-5497 


3.1346 


30.9 


97-075 


749.91 


954.81 


29503.629 


5.5587 


3.1380 


310 


97-389 


754-77 


961.OO 


29 7Q I. 000 


5.5678 


3.I4I4 


311 


97.704 


759-65 


967.21 


30080.231 


5.5767 


3.1448 


31-2 


98.018 


764-54 


973-44 


30371.328 


5-5857 


3.1481 


31.3 


98.332 


769-45 


979.69 


30664 . 297 


5.5946 


3.I5I5 


31.4 


98.646 


774-37 


985.96 


3O959.I44 


5-6035 


3-154* 


31-5 


98 . 960 


779-31 


992.25 


31255.875 


5.6124 


3-1582 


31-6 


99.274 


784.27 


998.56 


31554.496 


5.6213 


3-1615 


3i-7 


99.588 


789.24 


IOO4.89 


3I855-OI3 


5.6302 


3.1648 


31.8 


99.903 


794-23 


IOII.24 


32157.432 


5.6391 


3.1681 


31-9 


100.22 


799.23 


IOI7.61 


32461.759 


5-6480 


3.I7I5 


32.0 


100.53 


804.25 


IO24.OO 


32768.OOO 


5-6569 


3.1748 


32.1 


100.85 


809.28 


IO30.41 


33076.161 


5.6656 


3-1781 


32.2 


101.16 


8i4-33 


1036.84 


33386.248 


5.6745 


3.1814 


32.3 


101.47 


819.40 


IO43.29 


3369S.267 


5.6833 


3-1847 


32.4 


101.79 


824.48 


IO49.76 


34012.224 


5.6921 


3.1880 


32.5 


102.10 


829.58 


IO56.25 


34328.125 


5 7008 


3-i9 T 3 


32.6 


102.42 


834.69 


IO62.76 


34645.976 


5.7096 


3-1945 


32.7 


102.73 


839.82 


IO69.29 


34965.783 


5.7183 


3.I978 


32.8 


103.04 


844 . 96 


1075.84 


35287.552 


5.7271 


3.2010 


32.9 


103 . 36 


850.12 


I082.4I 


356H.289 


5-7358 


3.2043 


330 


103.67 


855.30 


I089.OO 


35937.000 


5.7446 


3-2075 


33-1 


103.90* 


860.49 


IO95.61 


36264.69I 


5.7532 


3.2108 


33-2 


104.30 


865.70 


1102.24 


36594.368 


5.7619 


3-2140 


33-3 


104.62 


870.92 


IIO8.89 


36926.O37 


5.7706 


3-2172 


33-4 


104.93 


876.16 


III556 


37259.704 


5-7792 


3.2204 


33-5 


105.24 


881.41 


1122.25 


37595-375 


5.7379 


3.2237 


33-6 


105.56 


886.68 


II28.96 


37933.056 


5.7965 


3.2269 


33-7 


105.87 


891.97 


II35.69 


38272.753 


5-8051 


3-2301 


33-8 


106.19 


897.27 


I 142 . 44 


38614.472 


5.8137 


3.2332 


33-9 


106.50 


902.59 


I I49. 21 


38958.219 


5.8223 


3-2364 


34- 


106.81 


907.92 


II56.OO 


39304.000 


5-8310 


3.2396 


34- 1 


107.13 


913.27 


Il62.8l 


39651.821 


5.8395 


3.2428 


34-2 


107.44 


918.63 


II69.64 


40001.688 


5 . 8480 


3-2460 


34-3 


107.76 


924.01 


II76.49 


40353.607 


5.8566 


3.2491 


344 


108.07 


929.41 


II83.36 


40707.584 


5.8651 


3 2522 



764 



EXPERIMEN TA L ENGINEERING. 
Constants — Continued. 



n 


nit 


4 


«? 


«• 


Vn 


s 


34.5 


108.38 


934.82 


1190.25 


41063.625 


5.8736 


3.2554 


34-6 


108.70 


940.25 


1197.16 


41421.736 


5.8821 


3.2586 


34-7 


109.01 


945.69 


1204.09 


41781.923 


5 . 8906 


3.26I7 


34-8 


iog-33 


951-15 


1211.04 


42144.192 


5.8991 


3 . 2648 


34-9 


109.64 


956.62 


1218.01 


42508.549 


5.9076 


3.2679 


35-o 


109.96 


962.11 


1225.00 


42875.000 


5-9161 


3-2710 


35-i 


110.27 


967.62 


1232.01 


43243.551 


5.9245 


3.2742 j 


35.2 


110.58 


973.14 


1239.04 


43614.208 


5.9329 


3-2773 


35-3 


110.90 


978.68 


1246.09 


43986.977 


5.9413 


3 . 2804 


35-4 


in. 21 


984.23 


1253.16 


44361.864 


5-9497 


3-2835 


35-5 


"I- 53 


989.80 


1260.25 


44738.875 


5.9581 


3.2866 


35-6 


in. 84 


995.38 


1267.36 


45118.016 


5.9665 


3.2897 


35-7 


112. 15 


1000.98 


1274.49 


45499.293 


5-9749 


3.2927 


35-8 


112.47 


1006 . 60 


1281.64 


45882.712 


5.9833 


3-2958 


35-9 


112.78 


1012.23 


1288.81 


46268.279 


5.9916 


3.2989 


36.0 


113. 10 


1017.88 


1296.00 


46656 . 000 


6 . 0000 


3-3019 


36.1 


H3-4I 


1023.54 


1303.21 


47045.881 


6.0083 


3-3050 


36.2 


113.73 


1029.22 


1310.44 


47437-928 


6.0166 


3 • 3080 


36.3 


114.04 


1034. 91 


1317-69 


47832.147 


6.0249 


3-3HI 


36.4 


H4-35 


1040.62 


13249 6 


48228.544 


6.0332 


3.3I4I 


39-5 


114.67 


1046.35 


1332.25 


48627.125 


6.0415 


3.3I7I 


36.6 


114.98 


1052.09 


I339.56 


49027.896 


6.0497 


3 • 3202 


36 7 


115-30 


1057.84 


1346.89 


49430.863 


6.0580 


3.3 2 32 


36.8 


115. 61 


1063.62 


1354.24 


49836.032 


6.0663 


3.3262 


36.9 


115.92 


1069.41 


1361.61 


50243.409 


6.0745 


3.3292 


37-0 


116.24 


1075.21 


1369.00 


50653.000 


6.0827 


3-3322 


37.i 


116.55 


1081.03 


1376.41 


51064. 811 


6 . 0909 


3-3352 


37-2 


116.87 


1086.87 


1383.84 


51478.848 


6.0991 


3-3382 


37-3 


117.18 


1092.72 


1391.29 


51895. 117 


6.1073 


3-3412 


37.4 


117.50 


1098.58 


1398.76 


52313.624 


6.1155 


3-3442 


37-5 


117. 81 


1104.47 


1406.25 


52734-375 


6.1237 


3.3472 


37-6 


118. 12 


1110.36 


1413.76 


53I57-376 


6.1318 


3.350I 


37-7 


118.44 


1116.28 


1421.29 


53582.633 


6.1400 


3.3531 


37-8 


118.75 


1122.21 


1428.84 


54010.152 


6.1481 


3.356I 


37-9 


119.07 


1128.15 


1436.41 


54439.939 


6.1563 


3-3590 


38.0 


119.38 


1134- 11 


1444.00 


54872.000 


6.1644 


3.3620 


38.1 


119.69 


1140.09 


1451.61 


55306.341 


6.1725 


3.3649 


38.2 


120.01 


1146.08 


1459-24 


55742.968 


6.1806 


3.3679 


38.3 


120.32 


1152.09 


1466.89 


56181.887 


6.1887 


3-3708 


38-4 


120.64 


1158.12 


1474.56 


56623.104 


6.1967 


3-3737 


38.5 


120.95 


1164.16 


1482.25 


57066.625 


6.2048 


3.3767 


38.6 


121.27 


1170.21 


1489.96 


57512.456 


6.2129 


3.3796 


_38-7 


121.58 


1176.28 


1497.69 


57960.603 


6.2209 


3-3825^ 



NUMERICAL CONSTANTS. 
Constants — Continued. 



765 



n 


wn 


4 


«« 


«3 


Tn 


3 


38.8 


121.89 


1182.37 


1505.44 


584II.072 


b.io&q 


3.3854 


38.9 


122.21 


1188.47 


1513.21 


58863.869 


6.2370 


3-3883 


39-o 


122.52 


1194.59 


1521.00 


593I9.OOO 


6.2450 


3.3912 


39- J 


122.84 


1200.72 


1528.81 


59776.471 


6.2530 


3-3941 


39-2 


123.15 


1206.87 


1536.64 


60236.288 


6.2610 


3.3970 


39-3 


123.46 


1213.04 


1544-49 


60698.457 


6.2689 


3-3999 


39-4 


123.78 


1219.22 


1552.36 


6II62.984 


6.2769 


3.4028 


39-5 


124.09 


1225.42 


1560.25 


6l629.875 


6.2849 


3.405& 


39-6 


124.41 


1231.63 


1568.16 


62O99.I36 


6.2928 


3-4085 ' 


39-7 


124.72 


1237.86 


1576.09 


62570.773 


6 . 3008 


3 -4i 14 


39-8 


125.04 


1244.10 


1584.04 


63044.792 


6.3087 


3.4142 


39-9 


125.35 


1250.36 


1592.01 


63521.199 


6.3166 


3.4171 , 


40.0 


125 . 66 


1256.64 


1600.00 


64OOO . OOO 


6.3245 


3.4200- 


40.1 


125.98 


1262.93 


1608.01 


6448I.2OI 


6.3325 


3.4228 


40.2 


126.29 


1269.23 


1616.04 


64964.808 


6.3404 


3.4256' 


40.3 


126.61 


1275-56 


1624.09 


65450.827 


6.3482 


3.4285. 


40.4 


126.92 


1281.90 


1632.16 


65939.264 


6.3561 


3.43I3; 


40.5 


127.23 


1288.25 


1640.25 


66430.125 


6.3639 


3-4341 


40.6 


127.55 


1294.62 


1648.36 


66923.416 


6.3718 


3- 4370 


40.7 


127.86 


1301.00 


1656.49 


674I9.I43 


6.3796 


3-4398 


40.8 


128.18 


1307.41 


1664.64 


679II.3I2 


6.3875 


3-4426 


40.9 


128.49 


1313.82 


1672.81 


684I7.929 


6-3953 


3.4454 


41.0 


128.81 


1320.25 


1681.00 


6892I.OOO 


6.4031 


3.4482 


41. 1 


129.12 


1326.70 


1689.21 


69426.53I 


6.4109 


3-45IO 


41.2 


129.43 


I333-I7 


1697.44 


69934.528 


6.4187 


3-4538- 


41-3 


129.75 


I339.65 


1705-69 


70444.997 


6.4265 


3.4566 


41.4 


130.06 


1346.14 


1713.96 


70957.944 


6.4343 


3-4594 


41.5 


130-38 


1352.65 


1722.25 


71473-375 


6.4421 


3.4622 


41.6 


130.69 


1359.18 


1730.56 


7I99I.296 


6.4498 


3.4650 


41.7 


131.00 


1365.72 


1738.89 


725II.7I3 


6-4575 


3.4677 


41.8 


131.32 


1372.28 


1747.24 


73034.632 


6.4653 


3.4705 


41.9 


131-63 


1378.85 


i755-6i 


73560.059 


6.4730 


3-4733 


42.0 


131.95 


1385.44 


1764.00 


74O88.O00 


6.4807 


3.4760 


42.1 


132.26 


1392.05 


1772.41 


746l8.46l 


6.4884 


3.4788 


42.2 


132.58 


1398.67 


1780.84 


75151.448 


6.4961 


3-4815 


42.3 


132.89 


1405.31 


1789.29 


75686.967 


6.5038 


3-4843 


42.4 


133.20 


141 1. 96 


1797.76 


76225.024 


6.5115 


3.4870 


42.5 


133-52 


1418.63 


1806.25 


76765.625 


6.5192 


3.4898 


42.6 


133-83 


1425-31 


1814.76 


77308.776 


6.5268 


3-4925 


42.7 


I34.I5 


1432.01 


1823.29 


77854.483 


6-5345 


3-4952 


42.8 


I34-46 


1438.72 


1831.84 


784.O2.752 


6.5422 


3-4Q8o 


42.9 


134.77 


1445.45 


1840.41 


78953.569 


6.5498 


3.5007 



766 



EXfERIMEN TAL ENGINEERING. 
Constants — Continued. 



n 


nn 


«* - 

4 


«» 


«» 


Vn 


h 


43 .0 


I35.09 


I452.20 


1849.00 


79507.000 


6-5574 


3-5034 


43-1 


135^40 


1458.96 


1857.61 


80062.991 


6.565I 


3.5061 


43-2 


135.72 


I465.74 


1866.24 


80621.568 


6.5727 


3.5088 


43-3 


136.03 


1472.54 


1874.89 


81182.737 


6.5803 


3-5II5 


43-4 


136.35 


1479-34 


1883.56 


81746.504 


6.5879 


3-5142 


43-5 


136.66 


1486.17 


1892.25 


82312.875 


6-5954 


3.5169 


43-6 


136.97 


I493-OI 


1900.96 


82881.856 


6.6030 


3.5196 


43-7 


137.29 


1499-87 


1909.69 


83453.453 


6.6IC6 


3-5223 


43-8 


137.60 


1506.74 


1918.44 


84027.672 


6.6182 


3-5250 


43.9 


137.92 


1513.63 


1927.21 


84604.519 


6.6257 


3-5277 


44.0 


138.23 


1520.53 


1936.00 


85184.000 


6.6333 


3.5303 


44.1 


138.54 


1527.45 


1944.81 


85766.121 


6.6408 


3 -533Q 


44.2 


138.86 


1534.39 


1953-64 


86350.888 


6.6483 


3-5357 


44-3 


139.17 


1541.34 


1962.49 


86938.307 


6.6558 


3.5384 


44.4 


139-49 


1548.30 


1971.36 


87528.384 


6.6633 


3- 54*o 


44-5 


139.80 


1555-28 


1980.25 


88121.125 


6 . 6708 


3-5437 


44.6 


140.12 


1562.28 


1989.16 


88716.536 


6.6783 


3-5463 


44-7 


140.43 


1569.30 


1998.09 


89314.623 


6.6858 


3-5490 


44-8 


140.74 


1576.33 


2007 . 04 


89915.392 


6.6933 


3-5516 


44.9 


141.06 


1583-37 


2016.01 


90518.849 


6 . 7007 


3-5543 


45-0 


I4L37 


1590.43 


2025.00 


91125.000 


6.7082 


3.5569 


45- 1 


141.69 


1597-51 


2034.01 


9I733-85I 


6.7156 


3-5595 


45-2 


142.00 


1604.60 


2043.04 


92345.408 


6.7231 


3-5621 


45-3 


142.31 


1611.71 


2052.09 


92959.677 


6.7305 


3-5648 


45-4 


142.63 


1618.83 


2061 . 16 


93576.664 


6.7379 


3-5674 


45-5 


142.94 


1625.97 


2070.25 


94196.375 


6-7454 


3- 5700 


45-6 


143.26 


1633.13 


2079.36 


94818.816 


6.7528 


3-5726 


45-7 


143-57 


1640.30 


2088.49 


95443.993 


6.7602 


3-5752 


45-8 


143-88 


1647.48 


2097 . 64 


96071.912 


6.7676 


3-5778 


45-9 


144.20 


1654.68 


2106.81 


96702.579 


6.7749 


3.5805 


46.0 


144.51 


1661.90 


2116.00 


97336.000 


6.7823 


35830 


46.1 


144.83 


1669.14 


2125.21 


97972.181 


6.7897 


3 5856 


46.2 


145.14 


1676.39 


2134.44 


98611.128 


6.7971 


3.5882 


46.3 


145.46 


1683.65 


2143.69 


99252.847 . 


6 . 8044 


3-59o8 


46.4 


145.77 


1690.93 


2152.96 


99897.344 


6.8117 


3-5934 


46.5 


146.08 


1698.23 


2162.25 


100544.625 


6.8191 


3.5960 


46.6 


146 . 40 


1705.54 


2171.56 


101194.696 


6.8264 


3-5986 


46.7 


146.71 


1712.87 


2180.89- 


101847.563 


6.8337 


3. 601 1 


46.8 


147.03 


1720.21 


2190.24 


102503.232 


6.8410 


3-6037 


46.9 


147-34 


1727-57 


2199.61 


103 161. 709 


6.8484 


3.6063 


47.0 


I47.65 


1734-94 


2209.00 


103823.000 


6.8556 


3.6088 


47.1 


147-97 


1742.34 


2218.41 


104487. in 


6.8629 


3 6114 


47.2 


148.28 


1749-74 ' 


2227-84 


105154.048 


6.8702 3.6139 



NUMERICAL CONSTANTS. 
Constants — Continued. 



767 



n 


nit 


4 


«a 


«8 


r n 


3 


47-3 


148.60 


1757.16 


2237.29 


IO5823.817 


6.8775 


3.6165 


47-4 


148.91 


1764.60 


2246.76 


IO6496.424 


6.8847 


36190 


47-5 


149.23 


1772.05 


2256.25 


I07I7I.875 


6.8920 


3.6216 


47.6 


149-54 


1779.52 


2265.76 


IO785O.I76 


6.8993 


3-6241 


47-7 


149-85 


1787.01 


2275.29 


IO853I.333 


6.9065 


3.6267 


47-8 


150.17 


1794- 51 


2284.84 


IO9215.352 


6.9137 


3.6292 


47-9 


150.48 


1802.03 


2294.41 


IO99O2 . 239 


6.9209 


3.63I7 


48.0 


150.80 


1809.56 < 


2304 . OO 


IIO592.OOO 


6.9282 


3-6342 


48.1 


151.11 


1817.11 


2313.61 


III284.64I 


6.9354 


3.6368 


48.2 


151.42 


1824.67 


2323.24 


III980.168 


6.9426 


3-6393 


48.3 


I5L74 


1832.25 


2332.89 


II2678.587 


6 . 9498 


3-6418 


48.4 


152.05 


1839.84 


2342.56 


"3379 -9°4 


6.9570 


3.6443 


48.5 


152.37 


1847.45 


2352.25 


1 14084. 125 


6 . 9642 


3.6468 


48.6 


152.68 


1855.08 


2361.96 


114791.256 


6.9714 


3.6493 


48.7 


153.00 


1862.72 


2371.69 


1 15501.303 


6.9785 


3.6518 


48.8 


153-31 


1870.38 


2381.44 


116214.272 


6.9857 


3-6543 


48.9 


153-62 


1878.05 


2391.21 


1 1 6930. 169 


6.9928 


3.6568 


49.0 


153.94 


1885.74 


2401.OO 


117649.000 


7 . 0000 


3.6593 


49.1 


154.25 


1893.45 


2410.81 


118370.771 


7.0071 


3.6618 


49-2 


154.57 


1901.17 


2420.64 


119095.488 


7.0143 


3.6643 


49-3 


154-88 


1908.90 


2430.49 


119823.157 


7.0214 


3.6668 


49.4 


155.19 


1916.65 


2440.36 


120553.784 


7.0285 


3.6692 


49-5 


155-51 


1924.42 


2450.25 


121287.375 


7.0356 


3.6717 


49.6 


155.82 


1932.21 


2460.16 


122023.936 


70427 


3-6742 


49-7 


156.14 


1940.00 


2470.09 


122763.473 


7.0498 


3.6767 


49.8 


156.45 


1947.82 


2480.04 


123505.992 


7.0569 


3.6791 


49.9 


156.77 


I955-65 


2490.OI 


124251.499 


7 . 0640 


3.6816 


50.0 


157.08 


1963.50 


2500.OO 


125000.000 


7.0711 


3.6840 


51.0 


160.22 


2042 . 82 


2601.00 


132651.000 


7.I4I4 


3.7084 


52.0 


163.36 


2123.72 


2704.OO 


140608.000 


7.2111 


3-7325 


53.o 


166.50 


2206.19 


2809 . OO 


148877.000 


7.2801 


3.7563 


54-o 


169 . 64 


2290.22 


2916.00 


157464.000 


7.3485 


3.7798 


55.o 


172.78 


2375.83 


3025.00 


166375.000 


7.4162 


3.8030 


56.0 


175 93 


2463.01 


3136.00 


175616.000 


7.4833 


3.8259 


57-0 


179.07 


255I-76 


3249.00 


185193.000 


7.5498 


3.8485 


58.0 


182.21 


2642.08 


3364.00 


195112.000 


7.6158 


3.8709 


59-o 


185.35 


2733-^7 


3481.00 


205379.000 


7.6811 


3.8930 


60.0 


188.49 


2827.44 


3600.00 


216000.000 


7.7460 


3.9149 


61.0 


191.63 


2922.47 


3721.00 


226981.000 


7.8102 


3-9365 


62.0 


194.77 


3019.07 


3844.00 


238328.000 


7.8740 


3.9579 


63.0 


197.92 


3117-25 


3969.00 


250047.000 


7-9373 


3-979 1 


64.0 


201.06 


3216.99 


4096.00 


262144.000 


8.0000 


4 . 0000 


65.0 


204.20 


3318.31 


4225.00 


274625.000 


8.0623 


4.0207 


66.0 


207.34 


3421 . 20 


4356.00 


287496.000 


8.1240 


4-0412 



768 



EXPERIMENTAL ENGINEERING. 
C on st ants — Continued. 



ft 


nir 


4 


«» 


«3 


Vh 


3 


67.0 


210.48 


3525.66 


4489 . OO 


3OO763.OOO 


8.1854 


4.0615 


68.0 


213-63 


3631.69 


4624.00 


314432.000 


8.2462 


4 


.0817 


69.0 


216.77 


3739-29 


4761 .00 


3285O9.OOO 


8 . 3066 


4 


1016 


70.0 


219.9I 


3848.46 


4900 . OO 


343000.000 


8.3666 


4 


1213 


71.0 


223.05 


3959-20 


5041.OO 


3579II.OOO 


8.4261 


4 


1408 


72.0 


226.19 


4071.51 


5184.OO 


37324S.OOO 


8.4853 


4 


1602 1 


73-o 


229.33 


4185.39 


5329.00 


389OI7.OOO 


8.5440 


4 


1793 


74.0 


232.47 


4300.85 


5476.OO 


405224.000 


8.6023 


4 


1983 


75-o 


235.62 


4417.87 


5625.OO 


42I875.OO0 


8 . 6603 


4 


2172 


76.0 


238.76 


4536.47 


5776.00 


438976.OOO 


8.7178 


4 


2358 


77.0 


241.9O 


4656.63 


5929.OO 


456533.OOO 


8.7750 


4 


2543 


78.0 


245.04 


4778.37 


6084 . OO 


474552.O00 


8. 318 


4 


2727 


79.0 


248.18 


4901.68 


624I.OO 


493039.0OO 


8.8882 


4 


2908 


80.0 


25I.32 


5026.56 


6400.OO 


512000.000 


8-9443 


4 


3089 


81.0 


254-47 


5153-or 


6561.OO 


53I44I.OOO 


9.0000 


4 


3267 


82.0 


257-61 


.5281.03 


6724.OO 


55I368.OO0 


9-0554 


4 


3445 


83.0 


260.75 


5410.62 


6889.OO 


57I787.OO0 


9. 1 104 


4 


3621 


84.0 


263.89 


554I-78 


7056.OO 


592704.OOO 


9.1652 


4 


3795 


85.0 


267.03 


5674.50 


7225.OO 


6I4I25.000 


9-"i95 


4 


3968 


86.0 


270.17 


5808.81 


7396.OO 


636O56.OOO 


9.2736 


4 


4140 


87.0 


273-32 


5944.69 


7569.OO 


6585O3.OOO 


9-3274 


4 


43io 


8S.0 


276.46 


6082.13 


7744.OO 


68I472.000 


9.3808 


4 


4480 


89.0 


279.60 


6221.13 


7921.OO 


7O4969.OOO 


9.4340 


4 


4647 


90.0 


282.74 


6361.74 


8IOO.OO 


72900O.OOO 


9.4868 


4 


4814 


91.0 


285.88 


6503.89 


8281.OO 


75357I.OOO 


9-5394 


4 


4979 


92.0 


289.02 


6647.62 


8464 . OO 


7786S8.000 


9-59*7 


4 


5144 


93-o 


292.17 


6792.92 


8649 . OO 


804357.000 


9-6437 


4 


5307 


94.0 


295-31 


6939, 78 


8836.OO 


83O584.OOO 


9.6954 


4- 


5468 


95-o 


298.45 


7088.23 


9025.OO 


857375.000 


9.7468 


4 


5629 


96.0 


301.59 


7238.24 


9216.OO 


884736.OOO 


9.7980 


4 


5789 


97.0 


304-73 


7389.83 


9409 . OO 


9I2673.000 


9.8489 


4 


5947 


98.0 


307-87 


7542.98 


9604.OO 


94II92.000 


9.8995 


4 


6104 


99.0 


311.02 


7697.68 


9801.OO 


97O299.OOO 


9.9499 


4 


6261 


100. 


314-16 


7854.00 


IOOOO.OO 


IOOOOOO.OOO 


10.0000 


4.6416 



LOGARITHMS OF NUMBERS. 



769 



III. 

LOGARITHMS OF NUMBERS. 



No. 





1 


2 


3 


4 


5 


6 


17 


8 


9 


IO 


0000 


0043 


0086 


0128 


0170 


0212 


0253 


0294 


0334 


0374 


11 


0414 


o453 


0492 


0531 


0569 


0607 


0645 


0682 


0719 


°755 


12 


0792 


0828 


0864 


0899 


0934 


0969 


1004 


1038 


1072 


1 106 


13 


1 139 


'"73 


1206 


1239 


1271 


1303 


1335 


1367 


1399 


1430 


*4 


1461 


1492 


i5 2 3 


*553 


1584 


1614 


1644 


1673 


1703 


1732 


15 


J 761 


1790 


18I8 


1847 


1875 


1903 


1931 


1959 


1987 


2014 


16 


2041 


206S 


2095 


2122 


2148 


2175 


2201 


2227 


2253 


2279 


3 


2304 


2330 


2355 


2380 


2405 


2430 


2455 


2480 


2504 


2529 


2553 


2577 


2601 


2625 


2648 


2672 


2695 


2718 


2742 


2765 


19 


2788 


2810 


2833 


2856 


2878 


2900 


2923 


2945 


2967 


2989 


20 


3010 


3032 


3054 


3075 


3096 


3"8 


3i39 


3160 


3181 


3201 


21 


3222 


3243 


3263 


3284 


3304 


3324 


3345 


3365 


3385 


3404 


22 


3424 


3444 


3464 


3483 


3502 


3522 


3541 


3560 


3579 


3598 


23 


3617 


3636 


3655 


3674 


3692 


3711 


3729 


3747 


3766 


3784 


24 


3802 


3820 


3838 


3856 


3874 


3892 


3909 


3927 


3945 


3962 


25 


3979 


3997 


4014 


4031 


4048 


4065 


4082 


4099 


4116 


4i33 


26 


415° 


4166 


4183 


4200 


4216 


4232 


4249 


4265 


4281 


4298 


27 


43H 


433o 


4346 


4362 


4378 


4393 


4409 


4425 


4440 


445 6 


28 


4472 


4487 


4502 


45 l8 


4533 


4548 


4564 


4579 


4594 


4609 


29 


4624 


4639 


4654 


4669 


4683 


4698 


4713 


4728 


4742 


4757 


30 


477i 


4786 


4800 


4814 


4829 


*4843 


4857 


4871 


4886 


4900 


31 


4914 


4928 


4942 


4955 


4969 


4983 


4997 


501 1 


5024 


5038 


32 


5°5i 


5065 


5079 


5092 


5105 


5"9 


5^2 


5H5 


5 J 59 


5172 


33 


5185 


5198 


5211 


5224 


5237 


5 2 5° 


5263 


5276 


5289 


5302 


34 


5315 


5328 


5340 


5353 


5366 


5378 


5391 


5403 


54i6 


5428 


35 


544i 


5453 


5465 


5478 


549o 


55° 2 


55H 


5527" 


5539 


555i' 


36 


5563 


5575 


5587 


5599 


561 1 


5 62 3. 


,5635 


5 6 47 


5658 


5670 


37 


56S2 


5 6 94 


570S 


5717 


5729 


574o- 


5752 


5763 


5775 


5786 


38 


5798 


5809 


5821 


5832 


5843 


5855 


5866 


5877 


5888 


5899 


39 


59i 1 


5922 


5933 


5944 


5955 


5966 


5977 


5988 


5999 


6010 


40 


6021 


6031 


6042 


6053 


6064 


6075 


6085 


6096 


6107 


6117 


4 1 


6128 


6138 


6149 


6160 


6170 


6180 


6191 


6201 


6212 


6222 


42 


6232 


6243 


6253 


6263 


6274 


6284 


6294 


6304 


6314 


6325 


43 


6335 


6345 


6355 


6365 


6375 


63S5 


6395 


6405 


6415 


6425 


44 


6435 


6444 


6454 


6464 


6474 


6484 


6493 


6503 


6513 


^6522 


45 


6532 


6542 


6551 


6561 


65 7 1 


6580 


6590 


6599 


6609 


6618 


46 


6628 


6637 


6646 


6656 


6665 


6675 


6684 


6693 


6702 


6712 


47 


6721 


6730 


6739 


6749 


6758 


6767 


6776 


6785 


6794 


6803 


48 


6812 


6821 


6830 


6839 


6848 


6857 


6866 


6875 


6884 


6893 


49 


6902 


691 1 


6920 


6928 


6937 


6946 


6955 


6964 


6972 


6981 


50 


6990 


6998 


7007. 


7016 


7024 


7°33 


7042 


7°5° 


7059 1 


7067 


5i 


7076 


7084 


7093 


7101 


7110 


7118 


7126 


7*35 


7H3 


7 X 5 2 


52 


7160 


7168 


7177 


7185 


7*93 


7^02 


7210 


7218 


7226 


7 2 35 


53 


7 2 43 


7251 


7259 


7267 


7275 


7284 


7292 


7300 


73o8 


73i6 


54 


7324 


7332 


7340 


7348 


735 6 


7364 


7372 


738o 


7388 


7396 


No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 



770 



EXPERIMENTAL ENGINEERING, 
Logarithms of Numbers — Continued. 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


55 


7404 


7412 


7419 


7427 


7435 


7443 


745i 


7459 


7466 


7474 


56 


7482 


7490 


7497 


75°5 


75J3 


7520 


7528 


7536 


7543 


755i 


57 


7559 


•7566 


7574 


7582 


7589 


7597 


7604 


7612 


-7619 


7627 


58 


7634 


7642 


7649 


7657 


7664 


7672 


7679 


7686 


7 6 94 


7701 


59 


7709 


7716 


7723 


773i 


7738 


7745 


7752 


7760 


7767 


7774 


60 


7782 


7789 


7796 


7803 


78ro 


7818 


7825 


7832 


7839 


7846 


61 


7853 


7860 


7868 


7875 


7882 


7889 


7896 


7903 


7910 


7917 


62 


7924 


793i 


7938 


7945 


795 2 


7959 


7966 


7973 


7980 


7987 


63 


7993 


8000 


8007 


8014 


8021- 


8028 


8035 


8041 


8048 


8055 


64 


8062 


8069 


8075 


8082 


8089 


8096 


8102 


8109 


8116 


8122 


65 


8129 


8136 


8142 


8i49 


8156 


8162 


81.69 


8176 


8182 


8189 


66 


8195 


8202 


8209 


8215 


8222 


8228 


8235 


8241 


8248 


8254 


67 


8261 


8267 


8274 


8280 


8287 


8293- 


.8299 


8306 


8312 


8319 


68 


8325 


8331 


8338 


8344 


8351 


8357 


8363 


8370 


8376 


838'2 


69 


8388 


8395 


8401 


8407 


8414 


8420 


8426 


8432 


8439 


8445 


70 


8451 


8457 


8463 


8470. 


8476 


8482 


8488 


8494 


8500 


8506 


71 


8513 


8519 


8525 


8531 


8537 


8543 


8549 


8555 


8561 


8567 


72 


8573 


8579 


8585 


8591 


8597 


8603 


8609 


8615 


8621 


8627 


73 


8633 


8639* 


8645 


8651 


8657 


8663 


8669 


8675 


8681 


8686 


74 


8692 


8698 


8704 


8710 


8716 


8722 


8727 


8733 


~8 7 39 


8745 


75 


8751 


8756 


8762 


8768 


8774 


8779 
8837 


8785 


8791 


8797 


8802 


76 


8808 


8814 


8820 


8825 


8831 


8842 


8848 


8854 


8859 


77 


8865 


8871 


8876 


8882 


8887 


8893 


8899 


8904 


8910 


8915 


78 


8921 


8927 


8932 


8938 


8943 


8949 


8954 


8960 


8965 


8971 


79 


8976 


8982 


8987 


8993 


8998 


9004 


9009 


9015* 


9020 


9025 


80 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 


81 


9085 


9090 


9096 


9101 


9106 


9112 


9117. 


9122 


9128 


9133 


82 


9138 


9H3 


9149 


9154 


9159 


9165 


9170 


9175 


9180 


9186 


83 


9191 


9196 


9201 


9206 


9212 


9217 


9222 


9227 


9232 


9238 


B4, 


9243 


9248 


9253 


9258 


9263 


9269 


9274 


,9279 


9284 


9289 


85 


9'294 


9299 


9304 


93°9 


93*5 


9320 


9325" 


9330 


9335 


9340 


86 


9345 


935° 


9355 


9360 


9365 


9370 


9375 


9380 


9385 


9390 


87 


.9395 


9400 


9405 


9410 


94i5 


9420 


9425 


9430 


9435 


9440 


88 


9445 


945° 


9455 


9460 


9465 


9469 


9474 


9479 


9484 


9489 


85 


9494 


9499 


95/>4 


95°9~ 


95*3 


9518 


95 2 3 


9528 


9533 


9538 


90 


9542 


"9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 


91 


959o 


9595 


9600 


9605 


9609 


9614 


9619 


9624 


9628 


9633 


92 


9638 


9643 


9647 


9652 


9657 


9661 


9666 


9671 


9675 


9680 


93 


9685 


9689 


9694 


9699 


9703 


9708 


9713 


9717 


9722 


9727 


94 


9731 


9736 


974i 


9745 


975° 


9754 


9759 


9763 


9768 


9773 


95 


9777 


9782 


9786 


9791 


9795 


9800 


9805 


9809 


9814 


9818 


96 


9823 


9827 


9832 


9836 


9841 


9845 


9850 


9854 


9859 


9863 


97 


9868 


9872 


9877 


988 r 


9886 


9890 


9894 


.9899 


9903 


9908 


98 


9912 


.9917 


9921 


9926 


993o 


9934 


9939 


9943 


9948 


995 2 


99 


9956 


9961 


9965 


9969 


9974 


9978 


9983 


9987 


9991 
8 


9996 
9 


No. 





1 


2 


3 


4 


5 


6 


7 



LOGARITHMIC FUNCTIONS OF ANGLES. 



771 



IV. 

LOGARITHMIC FUNCTIONS OF ANGLES. 



Angle. 



0° 0' 

o° 10' 
o° 20' 
o° 30' 
o° 40' 

o° 5<y 

1° 0' 

1° 10' 

i° 20' 
i° 30' 

i° 40' 

i° 50' 

2° . 0' 

2 C IO' 
2° 20' 
2° 30' 
2° 40' 
2° 50' 

3° 0' 

3 -10' 
3°. 20 A 
3° 30'. 
.3° 4o' 
3°. So' 
,40 / 

4 10' 
4 20' 
4° 3o' 
4° 40' 
4°50 / . 
5°0' 

5°' ic/ 
5 20'. 
5° 3o' 
.5° 4o' 
5° So' 
6° 0' 



6° 


10' 


6° 


2C/ 


6° 


30'. 


6° 


40' 


6° 


50' 


7° 


0' 


7° 


10' 


7° 


20 r 


7°' 


SO' 



Sin. 




•5776 
.6097 

•6397 
.6677 
.6940 



8. 7 ] 



.7423 
.7645 
.7857, 
.8059 
.8251 

.8436 



.8613 
.8783 
.8946 
.9104 
•9256 
8-94Q3 

•9545 
.9682 
.9816 

•9945 
,9.0070 



9.0192 



.0311 

;0426 

'' -°539 
. .0648 

•0755 

9-0859 

.0961 

.I060 

"57 
Cos. 



D. 1'. 



301. 1 
176.O 
125.0 
• 96.9 

79-2 
. .6^9 

58.0 

5 r i 

45.8 

4i-3. 
•37-8 
•34-8 
32.1 
30.0 
28.0 
. 26.3 
24.8 

' 23.5 
22.2 
21.2 

'20.2 
19.2 
18.5 
17.7 
17.0 

. 16.3 
15.8 
15.2 
14.7 
14.2 

13-7 
13-4 
12.9 
12.5 
12.2 

1 1,9 
"•5 
"•3 
10.9 
10.7 
10.4 
10.2 

9-9 
9-7 

D.l'. 



Cos. 



D. 1'. 



.0000 
•OOOO 
.OOOO 
.OOOO 
.OOOO 



9^999 

'•9999 

•9999 

. -9999 

• ^998 

•9998 

9.9997 



,9997 
.9996 
.9996 
•9995 
-9995 



9-9994 
-9993 
-9993 
•9992 
.9991 

•9990 
9-9989 

.9989 
.9988 
.9987 
.9986 
•9985 
9.9983 



'-9982 
.9981 
.9980 
•9,979 
^9977. 



9-997 6 

•9975 
•9973 
.9972 

• .9971 
•9969 

9.9968 
.9966 
.9964 
•9963 
Sin. 



Tan. J>. V. Cot 



7-4 6 37 
.7648 

.9409 

8.0658 

.1627 



-2419 
.3089 
.3669 
.4181 
.4638 
•5053 



-5 431 

•5779 
.6101 
.6401 
.6682 
♦6945 
.7194 



■7429 
.7652 
.7865 
.8067 
.8261 



8.8446 
"T8624 

•8795 
.8960 
.91.18 
.9272 
8.9420 

•95 6 3 
.9701 
.9836 
.9966 
9-QQ93 
9.0216 

^0336 
•0453 
.0567 
.0678 
,.0786 
9.0891 



•0995 
.1096 

•"94 

Cot. 



301. 1 

176.I 

I24.9 

96.9 

,79-2 

67.0 

58.0 

'51.2 

45-7 

' 41-5 

37-8 

.34-8 
.32-2 
30.0 
. 28.1 
26.3 
24.9 

23-5 
22.3 
21.3 
20.2 
19.4 
18.5 
,17.8' 
17.1 
16.5 
45.8 
15-4 
?4-8 

14-3 
13.8 

13-5 
1-3.0 
12.7' 
12.3 
12.0 
-*i. 7 
1 1.4 
11. 1 
10.8 
10.5 
10.4 
10.1 
9-8 

D.l'. 



2.5363 
.2352 
.0591 

I.9342 
•8373 



•758l 



.69II 

.6331 
.5819 
.5362 

4947 
•4569 



.4221 
.3899 
•3599 
.3318 
•3055 



.2806 



■2571 
.2348. 
.2135 
•1933 
•1739 



1-1554 



•1376 
.1205 
.1040 
.0882 
.0728 
1.0580 



0-0437 
' .0299 

.0164 

.0034 
0-9907 
09784 
. .9664 

•9547 
' -9433 

.9322 

.9214 



0.9109 

^9005" 

.8904 

.8806 

Tan. 



90° 0' 

89 50' 
89 40' 

89 30' 
89 20' 
89°ro' 
89° 6' 

88° so 1 
88° 40' 
58° 30' 
88° 20' 
88° 10' 
88° 0' 
87 50' 
S 7 ° 40' 
8 7 ° 3 c/ 
87 p 2o A 
87 10' 
87° 0' 
86° 50' 
86° 40' 
86° 30' 
86° 20' 
86° io / 
86° 0' 
8 5 °5o' 
85 40' 
S5 30' 
85 20' 
85 10' 
85° 0' 
84 50' 
84 40' 
8 4 ° 30' 
84 2d 
84 io' 
84° 0' 
83 50' 
83 40' 
8 3 °3o' 

8 3 °20' 

83 10' 
83° 0' 

82P 50' 
82 4 o' 
82°3o' 

Angle. 



7-J2 EXPERIMENTAL ENGINEERING. 

Logarithmic Functions of Angles — Continued. 



Angle. 


Sin. 


D.l'. 


Cos. 


D.l'. 


Tan. 


r>. v. 


Cot. 




7° 3o' 


9-1*57 


9-5 


9.9963 


.2 


9.1 194 


9-7. 


O.8806 


82° 30' 


7° 4o' 


.1252 


.9961 


.1291: 


.8709 


S2 20' 


70.50/ 
8° 0' 


•1345 
9-I436 


9-3 
9.1 

8-9. 

8.4 
8.2 •■ 
• 8.0 


•9959 


• 2 ' 
.2 


.1385 


9-4 
9-3 
9.1 

8-9 
8.7 
8 6 


.8615 


82° JO' 

82° 0' 


9-9958 


9-I478 


O.8522 


8 a 10'. 


.1525 


•995° 


<2 


•.1569 


~%V 


8i 5 o / 


8° 20' 


.1612 


•9954 


.2 
.2 


.1658 


.8342 


8i°- 4 o' 


8 ° 3 °: 


.1697 


•9952 


•1745 


•8255 


8i° 30' 


8° 40' 


.1781 


.9950 


.2 
.2 


•I8 3 I 


84 
8.2 


.8169 


8i° 20' 


8° 50' 


.1863 


•9948 


.1915 


.8085 


8i° 10' 


9° 0' 


9-1943 


7-9 

.7.6 

7-5 
7-3 
7-3 
7-1 
7.0 
•6.8 
'6.8' 


9-9946 


.2 


9.1997 


8.1 


0.8003 


81° 0' 


9 C 10' 


.2022 


•9944 


.2 


.2078 


80 


.7922 


8o c 50' 


9° 20' 


.2100 


•9942 


.2 
•2. 
.2 
.2 

•3-. 


.2158 


7.8 

7-7 
7.6 

7-4 
7-3 
7-3 
7-i 
7.0 

6.9. 
.6.8 


.7842 


8o° 40' 


9° 30' 


.2176 


•9940 


.2236 


•7764 


8o° 30' 


9 40' 


..2251 


•9938 


. ^313 


•7687 


8o°2o' 


9° 50' 

io° <y 

io° 10' 


.2324 


- -9936 

9-9934 

•9931 


' -2389 

9-2463. 

.2536 


.7611 


8o° 10' 
80° 0' 

79° SO' 


9-2397 
. .2468 


°JJ>JL 
•7464 


IO° 20' 


.2538 


.9929 


.2 

•3 

.2 • 


.2609 


•739i 


79° 40' 


io° 30' 


.2606 . 


.9927 


.2680 


.7320 


79° 30' 


io° 40' 


.2674 


6.6 


.9924 


.2750 


.7250 


79 20' 


io° 50' 


.2740 


6.6 


.9922 


•3" 

.2 


.28.19 


.7181 


79 10' 


11° 0' 


9.2806 


6.4 

,64 
6.3 
6.1 


9-99*9 


9.28"S7" 


6.6 


"oT"3~ 


79° 0' 


11° io' 


.2870 


.9917 


.3' 

.2 


~9~53 


67 
6.5 
6.4 
6-3. 
6-3 
6.1 


.7047 


7 So 5 c/ 


11° 20' 


•2934 


.9914 


.3020 


..6980 


7S 40' 


U° 30' 


.2997 


.9912 


3 

.2 


.■3085 


.6915 


78° 30' 


.11° 40' 


.3058 


' 6.! • 


.9909 


•3H9 


.6851 


78° 20' 


n° s& 


•3"9 


6.0 


• -9907 


•3 


_ 1 32I2' 


.67SS 


7S 10' 


12° 0' 


9-3I79 


5-9 
5.8 
5-7 

5 V 7 
5-6 

5-5 

5-4 

5-4 

5-3 

5-2 

5-2 

5-i 

5.0 

5-° 
.•4.9 

4-9 
4.8 

'4-7 


9.9904 


^3275 


0-6725 


78° 0' 


12° 16' 


•3238 


.9901 




.2 


•3336 


6.1 


" .6664 


77° 50' 


12° 20.' 


.3296 


•9899 


•3 
•3 
•3 
•3 
•3 
•3 
2 


-3397 


6!i 
5-9 
5-9 
5-8 

5-7 
5-7 
5-6 
5-5 
5-5 
5-4 

5-3 
5-3 
5-3 
5-i 
5-2 
5-i- 


.6603 


77° 40'- 


12° 30' 


•3353 


.9896 


•3458 


.6542 


77° 30' 


12° 40' 


.3410 


•9S93 


'■3S l 7 


•.64S3 


77 20' 


12° 50' 


•3466 


■ .9890 . 


■ -3576 


.6424 


77 '10' 


13° 0' 


9-3521. 


"9^887 


9-3634 


0.6366 


.77° 0' 


13° 10' 


•3575 


.0884 


.3691 


"^6309 


76° 50' 


13° 2d 


.3629 


.9S81 


•3748 


.6252 


76° 40' 


if 30' 


.36S2 


.9873 


—3804 


.6196 


76° 30' 


'3° 40' 


•3734 


.9875 


•3 
•3 
•3 
•3 


.3859 


.6141 


76° 20' 


13° 50' 


.3786 


-9872 


_l39i£ 


.60S6 


76 10' 


14° 0' 


9-3837 


9.9869 


9.396S 


0.C032 


76° 0' 


14 . 10' 


•3887 


"^9866" 


.4021 


•5979 


75° 50' 


1 4° 20' 


•3937 


.9863 


.4074 


.5926 


75° 4o' 


14° 30' 


.3986 


.9859 


•4 
•3 
•3 
•4 


.4127 


.5S73 


75°'3o' 


14° 40' 


•4035 


.9856 


. .4178 


.5822 


75° 20' 


14° 50' 
15° 0' 


•4083 
9-4130 


.9853 


.4230 


•5770 
o-57i9 


75° 10' 
75°" 0' 


9.9849 


9.4281 




Cos. 


D.l'. 


Sin. 


D.l'. 


Cot. 


D.l'. 


Tan. 


Angle. 



LOGARITHMIC FUNCTIONS OF ANGLES. 
Logarithmic Functions of Angles — Continued. 



773 



Angle. 


Sin. 


D.-l'. 


Cos. 


D. 1'. 


Tan. 


r>. i'. 


Cot. 




15° 0' 
i 5 ° io' 


9.4130 


4-7- 
4-6: 
4.6 

. 4-5- 
4-5" 

44. ' 
4.4 


9.9849' 


•3 
•3 
•4 
•3 
•4 
•4. 
•3 
•4 


9.4281 


5-o- 

5.0 

4-9 

4-9/ 

4.8: 

4.8,:' 

4-7 
4.7 


o-57*9 

,5669 


75° 0' 
74°5o' 


•41.77 


.9846 


.•4331 


i 5 ° 20' 


.4223 


•9843 


.4381 


,5619 


,74° 40' 


15° 30' 

15° 40' 


.4269 
4314 


.9839 
■•',9836 


•4430 
•4479 


•5570 
•552i. 


74°: 30' 

74° 2c' 


15° 50' 
16° Q' 


•4359- 
9.4403 


.9832. 


•4527 


•5473 
0.5425 


74° 10' 

74° 0' 


9.9828 


9-4575 


i6 c 10' 


•4447 


.9825 


.4622 


•5378. 


73° 5°' ' 


1 6° 20' 


•4491, 


4-4.. 


.9821 


.4669 


•5331 


73° 40' 


1 6° 30' 


•4533 


4.2 

4-3. 
4.2 

4.1' 

4.1 

4-1. 

4 A- 

4-0. 

4.0 
3-9 
3-9 

3-8 
3-8 
' 3-7 
3-8 
3-6 

3-7. 

3-6- 

3-6 

3-5 

3-6 

3-5 

3-4 

3-4 

3-4 

3-4 

3-3 

3-3. 

3-3 

3-3 

3-2 

3-2 

31 

3-2. 

3-i ' 

3-i 
3-o 


•9817 


•4 
'•3- 


• -47 f 6 


4-7 ■ 
4-6 
4-6 
•4:5 
*5 

4-5 

44 . 

44 

44 

4-3 

4-3 

4.2 

4.2 

4.2 

4.2 

4.1 

4.1 

t°o 

4.0. • 

4.0 

4.0 

3-9 • 

3-9 
3-8 
3-9 
3-8 
3-S 

3-7 
3-8 
3-7 
3-7 


•5284. 


73° 3o' 


1 6°. 40' 


•4576 


.9814 


.4762 


•5238 


73 20' 


1 6° 50/ 

17° 0' 
1 7 10' 


.4618 
9.4659 


.9810 


•4 
•4.. 
•4"' 
.,4 . 
•4. 
•4 . 
•4 ' 
•4 
•4 - " 

•4 
.4 . 
•5 
. -4 
.4 ■ 

•5 
•4 
•5 

•4 • 
•5 • 
•4 

•5. 
•4 : 
•5 
••5. 

•5- 
•4 

•5 
•5 
•5 
•5 
•5 
•5 
•5 
.6 
•5 

D. 1'. 


' .480*8 


•5192 


73° 10' 
73° 0' 
7 2 ° 50' 


9.9806 
.9802 


94853! 


0.5147 


.4700' 


• .4898: 


.5102 


1 7 '20' 


.4741 • 


.9798 


4943 


•5057 


7 2° 40' 


170 30' 


4781 


•9794 


• 4987 


•5 OI 3 


72° 30' 


17° 4 o' 


.4821 


•9790 


• -5 3i 


.4969 


72° 20' 


[7° 50' 


.4861 


.97S6 


•5075 


4925- 


72° IO' 


18° 0' 


9.4900 


9.9782 


9.51 18 


0.4882 


72° 0' 


18° io' 

1 8° 20' 


•4939 
•4977 


-.9778 
•9774 


.5161 
•5203 


4839 
4797 


7.1° 50; 
71° 40' 


iS° 30' 


•5°i5 


•9770 ' 


•5245 


4755 


71 30' 


1 8° 40' 


.5052 


•9765 


.5287 


4713 


71° 20' 


1 8° 50' 


.5090 


.9761 


•5329 


.4671 


71° 10' 


19° 0' 

19° 10' 


9.5126 
"5163" 


_<H>757 
•9752 


9-537Q 


04630 
4589 


71° 0'. 
70° 50' 


.5411 


19 20' 


•5' 99 


' .9748 


•5451 


4549 


70 40' 


1 9 30' 
19° 40' 


•5235 
• -5270 


•9743 
•9739 


•.•5491 
•5531 


.4509- 
.4469 


70 30' 

7O 20' 


19° 50' 
20° 0'" 


.5306 


•9734 


•557i 
9,5611 


4429 
0.4389 


70° I& 

70° 0' 


9-5341 


9-9730 


2Q° IO f 


. -5375 


•9725 


••5 6 5° 


435° 


69° 50 7 


20° 2C/ 
20° 30' 


.5409. 
' -5443 


• .9721 
.9716 


.5689 
•5727 


431 1 

4273 • 


69 40' 
69° 30', 


20°. 40' 


•5477 


.9711. 


.5766 


4234 


69° 20' 


20° 50' 


•55IO 


.9706 


.5804 


.4196 


69° IO' 


21° 0' 


9-5543 


9.9702 


9.5842 


0.4158 


69° 0' 


21° IO' 


•5576 


.9697 


.5879 


.4121 


68° 56* 


21° 20' 


.5609 


..9692 


•5917 


4083 


68° 40^ 


21° 30' 


.5641 


.9687 


•5954 


.4046 


68° 30' 


21° 4 O f 


•5°73 


.96S2 


.5991 


.4009 


68° 2C/ 


21 50' 
22° 0' 


•57°4 


.9677 


.6028 


3-7 
3-6 

3-6 
3-6 
3-6 


•3972 


68° 10' 
68° 0' 


9-5736 


9.9672 


9.6064 


0.3936 


22° IO' 


•57^7 


.9667 


.6100 


.3900 


67° 50' 


22° 20 f 


.5798 


. .9661 


.6136 


.3864 


67° 40' 


22° 30' 


.5828 


.9656 


.6172 


.3828 


6 7 °3C/ 




Cos. 


X>.1'. 


Sin. 


Cot. 


D.l'. 


Tan. 


Angle. 



774 



EXPERIMENTAL ENGINEERING. 
Logarithmic Functions of Angles — Continued. 



Angle* 


Sin. 


D.l'. 


Cos. 


D.l'. 


Tan. 


D. 1'. 


Cot. 




22^ 30' 


9.5828 


3.1 

3-o 

3-o 
2.9 

3-0 
2.9 
2.9 
2.9 
2.8 


9.9656 


•5 

•5 


9.6172 


3-6 

3-5 
3-6. 

3-5 
3-4 
3-5 
3-4 
3-5 
3-4 
3-4 
3-3 
3-4 
3-3 
3-4 
3-3 
3-3 
•3-2 
3-3 
3-2 
3-3 
3-2 

3-2 
3.2 
3-i 
.3-2 
3-i 

•3-2 


O.3828 


6 7 ° 30' 


22° 40' 


.5859 


.9651 


.6208 


•3792 


67° 20' 


22° 50' 


_j889_ 


.9646 


.6243 


•3757 


67° 10' 


23° 0.' 


9-5919 


9.964O 


•5 

,6' 

•5 
.6 

•5 
.6 


9-6279 


0.3721 


67° 0' 


23° io' 


•5948 


^9635 


.6314 


..3686 


66° 50* 


23° 2o' 


.5978 


.9629 


.6348 


.3652 


66° 40' 


23° 30' 


.6007 


.9624 


••6383 


•3617 


66° 30' 


23° 40' 


.6036 


.9618 


.6417 


.3583 


66° 20' 


23° 50' 


.6065 


•9613 


;6 4 52 


•3548 


66° 10' 


24° 0' 


V6093 


2.8 


9.9607 


«5. 
.6 
.6 
.6 

•5 
.6 


9.6486 


Q-35 H 


66° 0' 


24° 10' 


.6121 


2.8 
2.8 
2.8 
2.7 
2.7 
2.7 

2-7 
2.7 

2.6 
2.6 
2.6 


.9602 


.6520 


.3480 


65° 50' 


24° 20' 


.6149 


•9596 


•6553 


•3447 


65° 40' 


24° 30' 


.6177 


.9590 


.6587 


•34U 


65° 30' 


24° 40' 


.6205 


.95 8 4 


.6620 


•3380 


65° 2o' 


24° 50' 


•6232 


•9579 


.6654 


•3346 


65° IO' 


25° 0' 


9.6259 


9-9573 


.6 


9.6687 


03313 


65° 0' 


25° 10' 


.62S6 


•95 6 7 


.6 
.6 


.6720 


.3280 


64° 50' 


25° 20' 


6313 


.9561 


.6752 


.3248 


64° 40' 


25° 30' 


.6340 


•9555 


.6 


.6785. 


•3215 


6 4 ° 30' 


25° 40' 


.6366 


•9549 


.6 
.6 . 


.6817 


•3183 


64° 20' 


25° 50' 


'6392 


•9543 


.685O 


•3150 


64° 10' 


26° 0' 


9.6418 


2.6 


9-953X 


•7 
.6 


"9T688T 


0.31 18 


64° 0' 


26° 10' 


~~ [6444 


2.6 

2.5 

2.6 


•953o 


.69I4 


.3086 


.63° 50' 


26° 20' 


.6470 


.9524 


.6 
.6 


.6946 


•3054 


63 40' 


26° 30' 


.6495 


.9518 


.6977 


•3023 


63° 30' 


26° 40' 


.6521 




.9512 


•7 
.6 


.7009 


.2991 


63° 20' 


26° 50' 


•6546 


2-5- 
. 2.4 


•95°5 


• 7°4Q 


.2960 


63° 10' 


27° 0' 
27° ic/ 


9-657 
• 6 595 


-2.5 
-•2.5 


9-9499 
.9492 


•7 • 
.6 


9.7072 


31 
31 
31 

? T 


0.2928 


63° 0' 

62° 50' 


•7io3 


27° 20' 


.6620 


.9486 


•7*34 


.2866 


62° 40' 


27° 30' 


.6644 


2.4 


•9479 


•7 
.6. 

•7 

•7 
.6 


.7165 


.2835 


62° 30' 


27° 40' 


.6668 


2.4 


•9473 


.7196 


J- 1 
3-o 
3-i 

3-0 
3-o 
3-i 
3-o 
30 
3° 


2804 


62° 20' 


27° 50' 
28° 0' 


.6692 
9.6716 


2.4 

2.4 
2.4 
2.3 


.9466 


.7226 
9-7257 


•2774 


62° 1 6' 
62° 0' 


9-9459 


Q-2743 


28° 16' 


T6740 


•9453 


•7- 
•7 
•7 
•7 
.7 


.7287 


•2713 


61° 50' 


28° .20' 


.6763 


.9446 


•7317 


.2683 


61° 40' 


28° 30' 


.6787 


2.4 


•9439 


7348 


.2652 


61° 3 c' 


28° 40' 


.6810 


2 -3 


.9432 


.7378 


.2622 


6l° 2G' 


28° 50' 


•6833 


2 -3 

2.3 

2.2 

2.3 

2.2 


•9425 


•74o8 


•2592 


61° 10' 


29° 0' 

29° jo' 


9.6856 
.6878. 


9-94^8 
.9411 


•7 
•7 
•7 
•7 
•7 
. .8. 


9-7438 


2.9 

3-o 
2.9 

3-o 

2.9 
2.9 


0.2562 
~^2533. 


61 °0' 

60° 50' 


.7467 


29° 20' 


.6901 


.9404 


•7497 


•2503 


60° 40' 


29° 30' 


.6923 


•9397 


.7526 


.2474 


60° 30'- 


29° 40' 


.6946 


2-3 


•9390 


•755° 


:2 4 44 


60° 20' 


29° 50' 
30° 0' 


.6968 


2.2 
2.2 


•9383 
9-9375 


.7585 


•2415 


60° io' 
60° 0' 


9.6990 


9.7614 


0.2386 


" 


Cos. 


D.l'. 


,Sin. 


D. 1'. 


Cot. 


D. 1 . 


Tan. 


Angle. 



LOGARITHMIC FUNCTIONS OF ANGLES. 
Logarithmic Functions of Angles — Continued. 



77S 



Angle. 


Sin. 


D.l>. 


Cos. 


D.l'. 


Tan. 


D.i'. 


Cot. 




30° 0' 

30° 10' 


9.6990 
.7012 


2.2 


9-9375 


•7 

•7 
.8 


9.7614 


3.0 
2.9 

2.8 


O.2386 
.2356 


60° 0' 

59° 50 7 


.9368- 


•7644 


30° 20' 


-7033 


2.2 


.9361 


•7673 . 


.2327 


59° 40' 


3O 30' 


•7055 




•9353 


•7 
.8 


.7701 


2.9. 
2.9 

2.9 
2.8 
2.9 
2.8 
2.9 
28 


.2299 


59° 30 7 


3 o° 40' 


7076 


2.1 


.9346 


•7730 


.2270 


59° 20' 


30° 50' 


.7097 




•9338 


•7 
.8 
.8 


•7759 


.2241 


59° 10' 


31° 0' 

31° 10' 


9-7"8 
7*39 


2.1 


9-9331 
•9323 


9.7788. 


0.22I2 


59° 0' 

58*50" 


.7816 


12184 


31° 20' 


.7160 


2.1 


•9315 


•7 
8 


•7845 


•2155 


58° 40' 


310 30/ 


.7181 


.9308 


•7873 


.2127 


58° 30 7 


31° 40' 


.7201 




.9300 


.8 


.7902 


.2098 


5 8° 20 7 


31° .50' 
32° 0' 


.7222 


2.0 . 
2.0 


.9292 
9-9284 


,8 
.8 


. -7930 


'2.8 
28 


.2070 
O.2042 


58° 10' 

58° 0' 


9.7242 


9-7958 


32° 10' 


.7262 


2.0 
2.0 


.9276 


.& 
8 


.7986 


2.8 
2.8 
2.8 


.2014 


57° 50' 


32°. 20' 


.7282 


.9268 


.8014 


.1986 


57° 40' 


32° 30' 


.7302 


.9260 


.8 


.8042 


.1958 


57° 30' 


32° 40' 


.7322 




.9252 


8 


.8070 


2-7 
2.8 

2.8 ' 


.1930 


57° 20' 


32° 50' 
33° 0' 


•7342 


1-9 

1-9 
2.0 
1.9 
1:9 
1.9 
1.9 
1,8 
1.9 
1.8 
1.9 
1.8 
1.8. 

1.8. ' 

fi.8 

1.8 

1.7 

r.8 

1.7 

1.8 


•9244 
9-9236 


.8 
8 


.8097 


•I903 

0.1875 


57° 10' 
57° 0' 


9-736I 


9.8125 


33° 10' 


.738o 


.9228 


•9 
8 


.8153 


2.7 
28 


.1847 


56° 50* 


33° 20' 


.7400 


•9219 


.8180 


.1820 


'56° 40' 


33° 3o' 


.7419 


.9211 


.8 
•9 
•8 
•9 
.8 
•9 
•9 
•9 
.8 

•9 
•9 
•9 
•9 
•9 
-9 
1 


.8208 


2-7 
2 8 


.1792 


56° 30' 


33° 40'. 


.7438 


-9203 


.8235 


•1765 


56° 20' 


33° 5^ 
34° 0' 

34° !<• 


'7457 

'9-7476 

•7494 


.9194- 


.8263 


2.7 
2.7 

2.7 

2.7 

2-7 
2.7 

2-7 
2 -7 

2-7 
2.7 
26 


•*737 
0.1710 


56° 10' 
56° 0' 

55° 5o' 


9.9186 


9.8290 


.9177 


.8317 


.1683 


34° *• 


•75*3 


.9169 


•8344 


,1656 


55° 40 


34° 3o' 


•753i 


.9160 


•8371 


.1629 


55° 3o' 


34° 40' 


•755° 


•9i5i 


. .8398 


.1JJ02 


55° 2c/ 


34° 50' 
35° 0' 


.7568 


.9142 


.8425 


•1575* 


■ 55 °i<y 

55° 0' 


9.7586 


9-9134 


9.8452 


0.1548 


35° 10' 


.7604 


.9125 


.8479 


.1521 


54° 50' 


35° ** 


.7622 


.9116 


.8506 


.1494 


54° 40 


35° 3o' 


.7640 


.9107 


•8533 


.1467 


54° 30! 


35° 40' 


•7657 


.9098 


•8559 


2.7 
2.7 
26 


.1441 


54° 20' 


35° 5°' 
36° 0' 


•7675 


.9089 


.8586 
"9.8613 


.1414 
0.1387 


54° 10' 
54® 0' 


9.7692 


9.9080 


36° 10' 


.7710 


1.7. 

1-7 

i-7 


.9070 


•9 
•9 


.8639 


2.7 
2.6 
2 6 


.1361 


,53° 50' 


36° 20' 


•7727 


.9061 


.8666 


•1334 


53° 40' 


36° 30' 


•7744 


.9052 


.8692 


,1308 


53° 3o' 


36° 40' 


.7761 


.9042 




.8718 


2.7. 
2.6. 
2.6 


.1282 


53° 20' 


36° 5 </ 

37° 0' 


•7778 
9-7795 


hi 

1-7 
1 6 


.9033 


■9 
1.0 

•9 


•8745 


•1255 


53° 10' 
53° 0' 


9.9023 


9.8771 


0.1229 


37° 10' 


.7811 




.9014 


.8797 


2.7 
2.6 


.1203 


52° 50' 


37° -20' 


.7828 


1.6 


.9004 


•9 


.8824 


.1176 


52° 40' 


37° 3o' 


•7844 


•8995 


.8850 


,1150- 


52° 3°* 




Cos. 


D.l'. 


Sin. 


D.l'. 


Cot. 


D. 1'. 


Tan. 


Angle. 



Jj6 EXPERIMENTAL ENGINEERING. 

Logarithmic Functions of Angles — Continued. 



Angle. 


Sin. 


D.l'. 


Cos. !D. 1'. 


Tan. 


D. 1'. 


Cot. 




37 o 30' 


9.7844 


i-7 
1.6 
1.6 

i-7 
1.6 


9.8995 


1.0 


9.8850 


2.6 
2.6 
2.6 
2.6 
2.6 
2.6 


0.1 150 


5 2 30' 


37° 4o' 


.7861 


. .8985 


1.0 
1.0 
1.0 

" 1 .0 


.8876 


.1124 


52° 20' 


37° 5o' 
38° 0' 
38° 10' 


9-7893 


- -8975 
9.8965 


.8902 


.1098 


52° lof 

52° 0' 

51° 50' 


9.8928 


0.1072 


.7910 


•8955 


•8954 


.1046 


3 S° 20' 


.7926 


i-5 
1.6 


.8945 


1.0 


.8980 


.1020 


51° 40' 


38° 30' 


.7941 


.8935 


1.0 


.9006 


2.6 


.0994 


51° 30' 


38° 40' 


•7957 


1.6 


.8925 


1.0 


' .9032 


2.6 


.0968 


51° 20' 


3 S° 50' 


•7973 


1.6 


•8915 


I.O. 


_j9?_5l_ 


2.6 


•0942 


51° 10' 


39° 0' 


9-7989 


i-5 
1.6 


9.8905 


1.0 


9.9084 


2.6 


0.0916 


51° 0' 


39° 10' 


.8004 


.8895 


I.I 

1.0 


.9110 


2-5 
2.6 
2.6 

2-5 
2.6 


.0890 


5°° 59' 


39° 20' 


.8020 


i-5 
i-5 
1.6. 

I -5 


.8884 


•9135 


.0865 


50° 40' 


39° 30' 


.8035 


; 88 74 


1.0 
I.I 
1.0 


.9161 


.0839 


50° 30' 


39° 40' 
39° 5°' 


.8050 
.8066 


.8S64 
. .8853 


.91 S7 
.9212 


.0813 

.0788 


50° 20' 
50° 10' 


40° (V 


9.8081 


i-5 

'•5 

1.4 

i-5 

i-5 
1.4 

i-5 

1.4 

i-5 
1.4 

i-4. 
.1.4 

'1.4 
1.4 
• -i-4 
14 
i-3 
1.4 

J -3 
1.4 
i-3 


9.8843 


I.I 


9-9^8 


2.6 


0.0762 


50° 0'.. 


40° 10' 


~ .8096 


.8832 


I.I 

I . I 


.9264 


2-5 
2.6 
2.6 

2-5 
2.6 

2-5 
2.6 


.0736 


49° 5°' 


4O 2o' 


.8111 


.8821 


.9289 


.0711 


49° 40' 


40° 30' 


.8125 


.8810 


1.0 
I.I 
I.I 
I.I 


•9315 


.0685 


49° 30' 


40° 40' 


.8140 


.8800 


•9341 


.0659 


49° 20' 


40° 50' 

41° 0' 


.8155 


.8789 
9,8778 


•9366 

9.9392 


•0634 

0.0608 


49° 10' 
49° 0' 


9.8169 


41° 10' 


.8184 


.8767 


1 .1 


.9417 


"^0583" 


4 8° 5 </ 


41° 20' 


.819S 


.8756 


I . I 


•9443 


2-5 
2.6 


•°5>7 


4 S° 40' 


4i° 30' 


.8213 


.8745 


1 .2 


.9468 


.0532 


48° 30' 


41° 40' 


.8227 


.S733 


► I.I 


•9494 


2.5 

2-5 
2.6 

2-5. 
2.6 


.0506 


48° 20' 


41° 50' 
42° 0' 
42° IO / 


•8241 
.8269 


.8722 

9871T 

.8699 


I.I 
1.2 

I _ 1 


~95 x 9 


.0481 

0.0456 


48° 10' 
48° 0' 

47° 50' 


9-9544 
•9570 


.0430 


42° 20' 


.8283 


.86S8 


1.2 


•9595 


.0405 


47° 40' 


42° 3 o' 


.8297 


.8676 


I.I 


.9621 


2-5 
2-5 
2.6 

2-5 
2-5 
2-5 
2.6 


.0379 


47° 30/ 


42° 40' 


.8311 


.8665 


1 .2 


.9646 


•0354 


47° 20' 


42° 50' 

43° 0' 

43° 10' 


.8324 

9-8338 

•S351 


.8653 


1.2 

. 1.2 

j j 


•967 ' 

9-9697 

.9722 


•0329 

0.0303 

.0278 


47° 10' 
47° 0' 
46° 50' 


9.8641 
.8629 • 


.13° 2o' 


.8365 


.8618 


1.2 


•9747 


.0253 


46° 40' 


43° 3o' 


.S378. 


.860-6 


1.2 


•9772 


.0228 


46° 30' 


43° 40' 


.8391 


• I -3 

1.4 

•*-3 

1 -3. 
.1-3 

'.'1.2 


.8594 


r.2 
i-3 
1.2 


.9798 


.0202 


46° 20' 


43° 50' 
44° 0' 
44° 10' 


.S405 

9.8418 

.8431 


.S5S2 

9-8569 

•8557 


.9823- 
9.9S48 
.9874 


2-5 
2-5 
2.6 


•0177 

0.0152 
.0126 


46° IO' 

46° 0' 

45° 5°' 


44° 20' 


.8444 


.8545 


1 .2 

i-3 
1.2 

I 3 
1.2 


.9899 


2-5 


.0101 


45° 40' 


44° 3o' 


•8457 


.8532 


. .9924 


2-5 
2-5 
2.6 

2-5 


.0076 


45° 3o' 


44° 40' 
44° 50' 
45° 0' 


.84C9 
.8482 


1-3 
1-3 


.8520 
.8507. 


•9949 
•9975 


.0051 
.0025 


45° 20' 
45° IP' 
45° 0' 


9.8495 


9-8495 


0.0000 


0.0000 




Cos. 


D.l'. 


Sin. 


r>. i'. 


Cot. 


D. V. 


Tan. 


Angle. 



NA TURAL FUNCTIONS OF ANGLES. 



777 



V. 



NATURAL FUNCTIONS OF ANGLES. 



A. 


Sin. 


Cos. 




A. 


Sin.- 


Cos. 1^ | A. 


Sin. 


Cos. 




0° 

10' 
20' 
So' 
40' 
50' 

l d 
10' 
20' 
30' 
40' 
SO' 
2° 
10' 
20' 
30' 
40' 
50' 
3 C - 
10' 
20' 
30; 
40' 
50' 
4° 
10' 
20' 
.30' 
40' 
50' 
5° 
10' 
20' 
30' 
40' 
50' 
6° 
10' 
20' 
30' 
i>' 
50' 

7° 
10' 
20' 
30' 


.OOOOOO 


I. OOOO 


90° 

SO,' 
40' 
30' 
20' 
10' 
89° 
50; 
40' 

3°' 
20' 
10' 
88° 
50; 
40' 
30' 
20' 
10' 

87° 

50' 
40' 

30' 
20' 
10' 
86° 

40' 
30' 

20' 
10' 

85° 
50' 
40' 
30' 
20' 
10' 
8-4° 

50' 
40' 
30' 

20 r 
IO' 

83 d 

50' 

40' 

•30' 


30' 
40' 

50' 

8°- 
10' 

20' 
30' 
40' 
50' 

9° 

10' 
20' 
^30' 
40' 
50' 
10° 
10' 
20' 

3°; 

40' 
5o' 
11° 

10' 

20 f 
30' 
40' 
50' 

12° 

10' 

20' 

30' 

40' 

5o' 

13 c 

10' 

20' 
30' 
40' 
50' 

14° 

10' 
20' 
3o' 
40' 
5o' 
15° 


•1305 
•1334 
.1363 


.99 14 

.99II 
.9907 


3°' 
20' 

82° 
50; 
40' 
30' 

20'. 
IO< 

81° 

50' 
40' 
30' 
20' 
'10' 
80f 

5 °; 
40' 
30' 
20' 
10' 

79 c 

5 °; 
40' 

30' 

20' 

10' 

78 c 

50; 
40 f 
30' 
20'- 
10' 

77 c 

50; 

40' 

30' 

20' 

10' 

76 c 

50; 

40' 

30" 

20' 
10' 

75° 


15° 

10' 

20' 
30' 
-40' 
50' 

16° 

.10' 

20' 
30' 
4 o' 
5o' 
17° 
10' 
20' 
30' 
40' 
50' 
.18° 
10'' 
20' 
30' 
40' 
50' 
19 c 
10' 

20' 

30' 
40' 
SO' 

20° 

10' 
20' 
30' 
40' 
50' 

21° 

10' 
20' 
30' 

40' 
5o' 
22° 
10' 
20' 
30' 


.2588 


. -9659 


75° 

.50' 

40' 

30'. 
20' 
10' 

74° 

5°; 

40' 

30' 
20' 
10' 

73° 

50; 

40' 

30' 

20' 

10' 

72° 

50; 

40'. 

30' 

20 r 
IO' 

71° 

50; 
40' 
30' 
20' 
10' 
70 c 

5 o; 
4 o' 
30' 
20' 
10' 

69° 

5°' 

40' 

30' 
20' 
10' 
68° 

50; 
40' 
3o' 


.OO2909. 
.005818 
.008727 
.OU635 
.014544 


I .OOOO 
I .OOOO 
I. OOOO 

.9999 

•9999 


.2616 
.2644 
.2672 
.2700 
.2728 


.9652 
,9644 
.9636- 
.9628 
.9621 


.1392 


•9903 


.1421 
.1449 
.1478 
•I507 
•1536 


.9899 
.9894 
.9890 
.9886 
.9881 


.017452 


.9998 


.2756 


.9613 


.02036 
.02327 
.02618 
.02908 
.03199 


.9998 
•9997 
•9997 
.9996 

•9995 


.2784 
.2812 
.2840 
.2868 
.2896 


..9605 
.9596 
.9588 
.9580 
•9572 


.1564 


.9877 


•1593 
.1622 
.1650 
.1679 
.1708 


.9872 
.9S68 
.9863. 
..9858 
•9353 


.03490 


•9994 


•2924 


•9563 


.03781 
.04071 
.04362 
.04653 
•04943 


•9993 
.9992 
•9990 
.9989 
.9988 


•2952 
.2979 
•3007 

•3035 

.3062 


•9555 
•9546 
•9537 
•9528 
•9520 


•1736 


.9848 


•1765 
.1794 
.1822 
.1851 
.1880 


.9843 
•9838 

•9333 
.9827 
.9822 


.05234 


.9986 


.3090 


•95 " 


•05524 
.05814 
.06105 

•06395 
.06685 


•9985 
•9983 
.9981 
.9980 
.9978 


.3118 

■3*45 
•3173 
.3201 

.3228 
.3256 

•3283 
■33" 
•3338 
•3365 

1.3J93 
•3_4£o 

•344 _ 8 
•3475 
•3502 
•35 2 9 
:35_57 
•3584 


.9502 
.9492 
•9483 
•9474 
•9465 

_945i 
.9446 
•9436 
.9426 
.9417 
•9407 
•9~397 
•9387 
•9377 
•9367 
•935 6 

_ : 934_6_ 
•9336 


.1908 


.9816 


•1937 
•1965. 
.1994 
.2022 
.2051 


.98LI' 
.9805 
. -9799 
•9793 
•9787 


.06976 


.9976 


.07266 
•07556 
.07846 
.08136 
.08426 


•9974 
.9971 
.9969 
19967- 
.9964 


.2079 


.9781 


.2108 
.2136 
.2164 
.2193 
.2221 


•9775 
.9769 

•9763 
•9757 
•975° 


.08716 


.9962 


.09005 
.09295 

•095 8 5 
.09874 
.10164 


•9959 
•9957 
•9954 
•995 l 
•9943 

•9945 


.2250 
.2278 
.2306 
•2334 
.2363 
£392 
.2419 

•2447 
.2476 
.2504 
•2532 
.2560 


•9744 

•9737 

•9730 

.9724 

.9717 

J?7J2_ 

_j97p3_ 

. .9696 

.9689 

.9681 

.9674 

.9667 


•10453 


.10742 
.11031 
.11320 
.11609 
.11898 


.9942 
•9939 
•9936 

•993 2 
.9929 


.3611 
•363S 
.3665 
.3692 
•37^9 


•9325 
•9315 
•9304 
.9293 
. 9 _2S 3 _ 

•9272 


.12187 


•9925 


•3746 


.12476 
.12764 
.13053 


.9922 
.9918 
.9914 


•3773 
.3800 

.3827 


.9261 
.9250 
•9239 


.2588 


•9659 




Cos. 


Sin. 


A. 




Cos. 


Sin. 


A. 




Cos. 


Sin. 


A. 



778 



EXPERIMENTAL ENGINEERING. 
Natural Functions of Angles— Continued. 



A. 


Sin. 


Cos. 




A. 


Sin. 


Cos. 




A. 


Sin. 


Cos. 1 


30' 

40; 

23° 

10' 
20' 

3<y 
40' 
50' 

24° 

10' 

20' 

30; 

40' 

5°' 

25° 

10' 

20' 

30' 

40' 

50' 

26 c 

10' 

20' 
30' 
40' 
50' 

27° 

10' 

20' 

30' 

40' 

50' 

28° 
10' 
20' 
30' 
40' 
50/- 

29° 

10' 

20' 

30'- 

40' 

50' 

30 a 


.3827 
•3854 
.3881 


•9239 
.9228 
.9216 


30; 

20' 
IO' 

67° 

50' 
40' 
30' 

20' 
IO' 

66° 

5 °; 
40' 

30; 

20' 

10' 

65° 

50; 
40' 
30' 
20' 
10' 
64° 
50; 
40' 
30; 
20' 
10' 
63° 
50; 
40' 
30' 
20' 
10' 
62° 

5 °; 
40' 

30' 

20' 

10' 

61° 

50; 
40'- 
3o' 
20' 
ia'. 
60° 


30° 

10' 
20 r 
30' 
40' 
SO' 

31° 

10' 

20' 
30; 
40' 
SO' 

32° 

10' 
20' 
30; 

5^ 
33° 

10' 

20' 
30; 
40' 
50' 
34° 
10' 
20' 
30' 
40' 
50' 
35° 
10' 
20' 
30' 
40' 
5o' 
36° 
10' 
20' 
3c/ 
40' 
50' 
37° 
10' 
act' 
30 


.5000 


.8660 


60° 

50; 

40' 
30' 

20' 

10' 

59° 

50; 
40' 
30' 
20' 
10' 
58° 

5 o; 
40' 
30' 
20' 
10'. 

57° 

50; 

40' 

3°' 
20' 
10' 
56° 

50; 
40' 
30' 
20' 
10' 
55° 
50; 
40' 
30' 
20' 
10' 
54° 

5o'. 
40' 
30' 

20 ; 
IO' 

53° 

50' 

40' 
30' 


3 <y 
40' 
50' 

38° 

IO' 

20^ 
30' 
40' 
50' 
39° 
10' 
20' 
30' 
40' 
50' 
40° 
10' 
20' 

40' 
50' 
41° 

10' 

20' 
30' 
40-' 
5o' 
42° 
10' 

20 7 
•30' 
40' 
SO' 

43° 

10' 
20' 
30' 
40' 
50' 

44° 
10' 
20/ 
3c/ 
40' 
50' 
45° 


.6088 
.6m 
.6134 


•7934 
.7916 
.7898 


30' 
20' 
10' 
52° 
50' 
40' 
30' 
20' 
10' 
51° 
50; 
40' 
30' 
20' 
10' 
50° 
S d 
40' 
30' 
20' 
10' 
49° 
50; 
40' 
30' 

20 r 
IO' 

48° 

50; 

4o' 

30' 

20' 

10' 

47° 

40> 
3o' 
26' 

!</ 

461° 

50' 
40' 
30' 

20 7 

ia' 

45° 


•5025 

•5°5° 
•5°75 
.5100 

•5125 


.8646 
•8631 
.8616 
.8601 
•8587 


•3907 


.9205 


•6i57 


.7880 


•3934 
.3961 

.3987 
.4014 
.4041 


•9194 
.9182 

.9171 
•9159 
.9147 


.6r8o 
.6202 
.6225 
.6248 
.6271 


.7862 
.7844 
.7826 
.7808 
^7790 


•5150 


•8572 


■5*75 
.5200 

•5225 
•5250 
•5275 


•8557 
.8542 
.8526 
•85 1 1 
.8496 


.4067 


•9135 


.6293 


.7771 


.4094 
.4120 
.4147 

.4173 
.4200 


.9124 
.9112 
.9100 
.9088 
•9075 


.6316 
.6338 
.6361 

•'6383 
.6406 


•7753 
•7735 
.7716 
.7698 
.7679 


•5299 


.8480 


•5324 
•5348 
•5373 
•5398 
•5422 


.8465 
.8450 

•8434 
.8418 
.8403 


.4226 


.9063 


.6428 


.7660 


•4253 
•4279 
•4305 
•4331 
•4358 


.9051 
.9038 
.9026 
.9013 
.9001 


.6450 
.6472 
.6494 
•6517 
•6539 


.7642 
.7623 
.7604 

•7585 
.7566 


•5446 


.8387 


•547i 
•5495 
•55*9 
•5544 
.5568 


.8371 
•8355 
•8339 
.8323 
.8307 


•4384 


.8988 


.6561 


•7547 


.4410 
4436 
.4462 
.4488 
•45*4 


.8975 
.8962 
.8949 
.8936 
•8923 


.6583 
.6604 
.6626 
-.6648 
.6670 


.7528 

•7509 
.7490 
.7470 
•745.1 


•5592 


.8290 


.5616 
.5640 
.5664 
.5688 
•5712 


.8274 
.8258 
.8241 
.8225 
.8268 


•4540 


.8910 


.6691 


•743i 


.4566 
.4592 
.4617 

4643 
.4669 


.8897 
.8884 
.8870 

. .8843 


•6713 
•6734 
.6756 
.6777 
.6799 


•74*2 
•7392 
•7373 
-•7353 
•7333 


•5736 


.8192 


.5760 

.5783 
.5807 

•5831 
•5854 


•8175 
•8158 
.8141 
.8124 
.8107 


.4695 


. .8829 


.6820 


•73M 


.4720 
.4746 
.4772 

•4797 
■ .4823 


.8816 
.8802 
.8788 

.8774 
.8760 


.6841 
.6862 
.6884 
.6905 
.6926 


.7294 
•7274 
•7254 
•7234 
.7214 


.5878 


.8090 


.5901 
•-5925 
•5948 
•5972 
•5995 


.8073 
.8056 
•8039 
.8021 
.8004 


.4848. 


.8746 


.6947 


•7193 


•4874 
.4899 

•4924 
•495° 
.•497S 


.8732 
.8718 
.8704 
.8689 
.8675 


.6967 
.6988 
.7009 
.7030 
.7050 


•7173 
•7153 
•7133 
.7112 
.7092 


.6018 


..7986 


.6041 
.606 s 
.6088 


.7969 
•7951 
•7934 


.5000 


.8660 


.7071 


.7071 




Cos. 


Sin. 


A. 




Cos. 


Sin. 


A. 




Cos. 


Sin. 


A. 



NATURAL FUNCTIONS OF ANGLES. 



779 



Natural Functions of Angles — Continued. 



A. 


' Tan. 


Cot. 




A. 


Tan. 


Cot. 1 


A. 


Tan. 


Cot. 


' 


0° 

id' 

20' 
30' 
40' 
50' 

1° 
10' 
20' 

30; 

40' 

50' 

2° 
1.0' 

20 ' 

30'- 

40' 

5o' 

3° 

10' 

20 f 
30; 

50' 

40 

IO' 

20' 
30' 
40' 
SO' 

5° 
10' 
20' 
30' 
40' 
50' 
6° 
10' 
20' 
3o' 
40' 
5o' 
7° 
10' 
20' 
30' 


.OOOOOO 


op 


90° 

50' 
.40' 
30' 
20' 
IO' 

89° 

5 °; 
40' 

30' 

20' 

10' 

88° 

5 °; 
40' 

30' 

•20' 

10' 

S7 C 

5 o; 
40' 

20' 

10' 

8G C 

50; 
40' 
3o' 
20' 
10' 

85° 

5 °; 
40' 

30' 

20' 

10' 

84° 

50;. 
40' 
30' 
20' 
10' 
S3 C 
50; 
40' 
3o' 


: 3 o< 
40' 
50' 
8° 
10' 
20' 

3°' 
40' 

5o' 

9° 

10' 

20' 

30' 

40' 

5o' 

10° 

10' 

20' 

3o' 

40' 

5o' 

11° 

10' 

20' 

3o' 

40' 

5o' 
12° 
■10' 
20' 
30' 
40' 
-50' 

13° 

10'., 

20' 

3o' 

40' 

5°' 

14° 

10' 

20' 

So'' 

40' 

50' 

15° 


'1317 
.1346 

■1376 


7-5958 
7.4287 
7.2687 


30' 
20' 
.IO' 

82° 

50' 
40' 

30' 

20 f 
IO' 

81° 

50; 
40' 

3°' 
20' 
10' 
80° 

50; 

40' 
30' 
20' 
10' 
79 c 
50; 
40' 
30' 
20' 
10' 
78° 
50; 
40' 
30' 
20' 
10' 
77° 
50' 
40' 
3o' 
20' 
10' 
76° 

50; 
40' 
30' 
20' 
10' 
75° 


15° 

IO' 
2C/ 
30' 
40' 

50' 

16 Q 

10' 
20' 
30' 
40' 
5o' 
17° 
10' 
20' 

30' 

40' 

50' 
18° 

10' 
20' 
30' 
40' 
5o' 
19° 
10' 
20' 
30' 
40' 
5o' 
20° 
10' 
20' 
30' 
40' 
50' 

21° 
10' 

2C/ 
30' 
40' 
50' 

22° 

IO 7 

20' 

30' 


.2679 


3-7321 


75° 

50' 
40' 
30' 
20' 
10' 
74c 

50; 
40' 
30' 
20' 
10' 
73°. 

50;: 
40'. 
30' 
20' 
10' 
72° 
5 c/ 
40' 
30' 
20' 
10' 
71 c 

5 °: 
40' 

30' 

20 ; 
IO' 

70 c 

50; 
40' 
30; 
20' 
10' 
69° 

5°: 

40' 

30' 

2o' 
IO' 

68° 

5°' 
40' 

30' 


.002909 
.005818 
.008727 
.01 1636 

.014545 


343-7737 

171.8854 
114.5887 

85-9398 
68.7501 


.2711 
.2742 

•2773 
.2805 
.2836 
.2867 


3.6891 
3.6470 
3-6059 
3-5656 

_3 : 5 2 Jn 
34874 

3-4495 
3.4124 

3-3759 
3-3402 
3-3052 


.1405 


7-i r 54 


•H35 
.1465 

•1495 
.1524 

•1554 

.1584 


6.9682 
6.8269 
6.6912 
6.5606 
6.4348 
6.3138 


•OI7455 


57.2900 


.02036 
.02328 
.02619 
.02910 
.03201 


49.1039 
42.9641 
38.1885 
34-3678 
31.2416 


.2S99 
.2931 
.2962 
.2994 
.3026 


.1614 
.1644 
■1673 
■I703 
■*733 


6.1970 
6.0844 

5-9758 
5.8708 
5.7694 


.03492 


28.6363 


•3057 
.3089 
.3121 

•3153 
•3185 

•3217 


3.2709 


•03733 
.04075 
.04366 
.04658 
.04949 


26.4316 
24.5418 
22.903S 
.21.4704 
20.2056 


3-237 1 
3.2041 
3.1716 

3-J397 
3.1084 


•i7 6 3 


5-67I3 


•1793 
.1823 

-1853 
.1883 

.1944 


5-5764 
54845 
5-3955 
5-3°93 
5- 2 257 
5-M46 


.05241 


19.081 1 


•3249 


3-0777 


•05533 
.05824 
.06 1 1 6 
.06408 
.06700 


18.0750 
17.1693 
16.3499 
15.6048 
14.9244 


.3281 
•33H 
•3346 
•3378 
•341 1 


3-0475 
3.0178 
2.9887 
2.9600 
2.9319 


.1974 
.2004 

•2035 
.2065 
.2095 


5.0658 
4.9894 

4-9I52 
4.8430 
4.7729 


.06993 


14.3007 


■JA43 
•.3476 
•35o8 
•3541 
•3574 

:1 6 _°.7 

•3640 

•3673 
•37o6 
•3739 
•3772 

•3839 
•3872 
.3906 
•3939 
•3973 
.4006 

.4040 

•4074 
.410S 
.4142 


2-9042 
2.8770 
2.8502 

2.8239 
2.7980 
2.7725 


.07285 

•07573 
.07S70 
.0S163 
.08456 


13.7267 
13.1969 
12.7062 
12.2505 
11.8262 


.2126 


4.704C 


.2156 
.2186 
.2217 
.2247 
.2278 


4-6382 
4-5736 
4-5 io 7 
4.4494 
4-3397 


.08749 


11,4301 


2-7475 
2.7228 
2.6985 
2.6746 
2.65 1 1 
2.6279 
2.6051 

2.5605 
2.5386 
2.5172 

2.4960 

T4751 


.09042 

•09335 
.09629 
.09923 
.10216 


11.0594 
10.7119 
10.3S54 
10.0780 
9.78S2 


.2309 


4-33I5 


•2339 
•2370 
.2401 
.2432 
.2462 


4-2747 
4.2193 
4-1653 
4.1126 
4.061 1 


.10510 


9-5 1 44 


.10805 
.11099 

.11394 
.11688 
.11983 


9-2553 
9.0098 
8.7769 

8-5555 
8.3450 


•2493 


4.0108 


.2524 

•2555 
.2586 
.2617 
.2648 


3-96i7 
3-9I36 
3.8667 
3.8208 
3.7760 


.12278 


8.1443 


.12574 
.12869 
.13.165 


7-9530 
7.7704 
7-5958 


2-4545 
2-4342 
2.4142 


.2679 


3-7321 




Cot. 


Tan. 


A. 




Cot. 


Tan. 


A. 




Cot. 


Tan. 


A- 



780 



EXPERIMENTAL ENGINEERING. 
Natural Functions of Angles — Continued. 



A. 


Tan. 


Cot. 




A. 


Tan. 


Cot. 




A. 


Tan. 


Cot. 




30' 
40' 
SO' 


4142 
4176 
4210 


2.4142 
2.3945 
2.3750 


30' 
20' 
IO' 

67° 

5 °: 
40' 

30' 

•20' 

10' 

66° 

50' 
40' 
30' 
20' 
10' 

65° 

5 °; 
40' 

30' 

20' 

10' 

64° 

5 °; 
40' 

3°' 

20 7 
IO' 

63° 

5 </ 
40' 
30' 
20' 
10' 
62° 

5 °; 
40' 

30' 

20' 

10' 

61° 

50; 
40' 

3°' 
20' 
10' 
60° 


30° 

10' 

20' 

3°' 
40' 
50' 
31° 

10' 

20' 
30' 
40' 
50' 

32° 
10' 
20' 
30; 
40' 
50' 

33° 

10' 
20' 
30' 
40' 
50' 

34° 

jo' 
20' 
20' 
40' 
50' 

35° 
10' 

20' 
30' 

4<y 
50' 

30° 

10' 
20' 
30' 
40' 
5o! 
37° 
10' 
20' 
3°' 


•5774 


I-732I 


60° 

50; 
40' 
30' 
20' 
10' 
59° 
50; 
40' 
30' 
20' 
10' 
58° 
50; 
40' 
30' 
20' 
10' 
57° 
50; 
40' 

3°' 
20' 
10' 
56° 

50; 
40' 
3°' 

2Q 7 
IO' 

55° 

40'' 

30' 

20' 

10' 

54° 

50; 

40' 

30' 

20' 

10' 

53° 
50; 
40' 
30' 


3o; 
40' 
50' 
38° 

IO' 
20 7 
30' 
4?' 
SO' 

39° 

10' 

20' 
30' 
40' 
50' 

40° 

10' 
20' 
30; 
4o' 
50' 

41° 

10' 

20' 
3o' 
40' 
50' 

42° 
.10' 
20' 
30' 
40' 
5o' 
43° 
10' 

20 f 
30' 
40' 
50' 

44° 
10' 
20' 
30; 
40' 
5o' 
45° 


•7673 
.7720 
.7766 


I.3032 
I.2954 
I.2876 


30' 

20 y 
IO / 

52° 

50; 

40' 

3°' 

20' 

10' 

51° 

50; 

40' 

30' 

20' 

to' 

5 °; 
40' 

30' 

20 ; 
IO' 

49° 

50' 
40' 
30' 
20' 
10' 
48° 
•50; 
40 ; 
30' 
20' 
10' 
47° 

40 7 
30; 
20' 
10' 

46° 

5 °; 

40' 

30' 
20' 
10' 

45° 


.5812 

.5851 
.5890 
•593o 
•5969 


I.7205 
I.7090 
I.6977 
I.6864 
1-6753 


23° 


4245 


2-3559 


.7813 


I.2799 


10' 
20' 
30' 
40' 
5o' 


4279 
43H 
4348 
4383 
4417 


2.3369 
2.3183 
2.2998 
2.2817 
2.2637 


.7860 
.7907 

•7954 
.8002 
.8050 


I.2723 
I.2647 
I.2572 
I.2497 
I.2423 


.6009 


1.6643 


.6048 
.6088 
.6128 
.6168 
.6208 


1.6534 
I.6426 
1. 63 19 
I.6212 
1. 6107 


24° 


445 2 


2.2460 


.8098 


1.2349 


10' 

20' 
30' 
40' 

5°' 


4487 
4522 

4557 
4592 
4628 


2.2286 
2.2113 

2.1943 
2.1775 
2.1609 


.8146 

.8195 
.8243 
.8292 
.8342 


I.2276 
I.2203 
I.2I3I 

I.2059 
1. 1988 


.6249 


I.6003 


.6289 

•6330 

•6371 
.6412 

•6453 


I.5900 
I.5798 
L I-5697 
!-5597 
1-5497 


25° 


4663 


2.1445 


8391 


I.1918 


iq'. 

20' 
30' 
40' 
50' 


4699 

4734 
4770 
4806 
4841 


2.1283 
2.1 123 

2.0965 
2.0809 
2.0655 


.8441 
.8491 
.8541 
.8591 
.8642 


1. 1847 
1. 1778 
1. 1708 
1. 1640 


.6494 


1-5399 


.6536 

•6577 
.6619 
.6661 
.6703 


1 -530i 
1.5204 
1. 5 108 
1-5013 
I-49I9 


26 c 


4877 


2.O503 


•8693 


1. 1504 


10' 
20' 
30' 
40' 

5o' 


4913 
495° 
4986 
5022 
5059 


2-0353 
2.0204 
2.OO57 
I.9912 
I.9768 


•8744 
.8796 
•8847 
.8899 
.8952 


1. 1436 
I. 1369 
1. 1303 
11237 
I.II71 


•6745 


1.4826 


.6787 
.6830 

.6873 
.6916 

•6959 


1-4733 
1. 4641 

I.4550 
I.4460 

1.4370 


27° 


5095 


I.9626 


.9004 


I.II06 


10' 
20' 
30' 
40' 
5o' 


5 J 32 
5 l6 9 
5206 

5243 
5280 


. 1 .9486 

1-9347 
1. 92 10 
1.9074 
1 .8940 


•9057 
9110 
.9163 

.9217 
.9271 


I.IO41 
I.0977 
1. 091 3 
I.0850 
I.0786 


.7002 


r.4281 


.7046 
.7089 

•7*33 
.7177 
.7221 


I-4I93 
1. 4 106 
1. 4019 

1-3934 
1-3848 


28° 


53i7 


1.8807 


•9325 


I.0724 


10' 
20' 

3°' 
40' 
50' 


5354 
5392 
543o 
5467 
55°5 


1.8676 
1.8546 
1.8418 
1.8291 
. 1.8165 


.9380 

•9435 
•9490 

•9545 
.9601 


1. 066 1" 
I.0599 
I.0538 
I.0477 
1. 041 6 


.7265 


I-3764 


•73io 

•7355 
.7400 

•7445 
.7490 


1.3680 
1-3597 
I-35H 
1.3432 
I-335 1 


29° 


5543 


1 .8040 


•9657 


1 -0355 


10' 
20' 
30' 
40' 
. 5o' 


5581 

5 6l 9 
5658 
5696 
5735 


1-7917 
1.7796 

r-7675 
I-755 6 
1-7437 


•9713 
.9770 

.9827 
.9884 
•9942 


1.0295 
1.0235 
1.0176 
1.0117 

1.0058 


•7536 


1.3270 


.7581 
.7627 
•7673 


1.3190 
1.3111 
1.3032 


30° 


5774 


1-7321 


1. 0000 


1. 0000 




Cot. 


Tan. 


A. 




Cot. 


Tan. 


A. 




Cot. 


Tan. 


A. 



COEFFICIENTS, STRENGTH OF MATERIALS. 



7 8l 



VI. 

TABLE OF COEFFICIENTS, STRENGTH OF MATERIALS. 



Cast-iron 

Average 

American ordnance 

Repeatedly melted 

Wrought-iron — 

Finest Low- j with grain. 

moor plates: \ across " . 

. , \ with " . 

Bridge-iron: \ „„_«.„ « 
& ( across 

Bars, finest 

Bars, ordinary 

Bars, soft Swedish 

Wire 

Steel— 

Mild-steel plates 

Axle and rail steel 

Crucible tool- " 

Chrome " 

Tungsten " 

Steel wire 

Piano-wire 

Copper — 

Cast 

Rolled 

Wire, hard drawn 

Brass 

Wire 

Gun-metal 

Phosphor bronze 

Zinc, cast. ... 

Zinc, rolled 

Tin 

Lead 

Timber — 

Oak 

White pine 

Pitch-pine 

Ash. 

Beech. 

Mahogany 

Stone — 

Granite 

Sandstone 

Limestone 

Brick 



Ultimate Stren 


nh. 


Moduli. 


Tons 


ser Square Inch. 


Tons per Sq 


. Inch. 


Tension. 


Com- 
pression. 


Shearing. 


Elasticity. 


Rig. 


T 


C 


S 


E 


Es 


7 

. 14 

15-20 


25-65 

42 

36-58 

60-75 


9-13 
II 


5 #00 

y to 
6000 


I3OO 

to 

2500 


27-29 




1 


' 




24 










22 






12,000 




IO - 
27-29 




- 18-22 


► to 

13,000 


5000 


25 


20 








19-24 










25-50 




J 


J 




26-32 




1 m 


) 




30-45 

40-65 

80 







12,000 
> to 


5000 

to 


72 




1 13,000 


5200 


70 




% 


J 




150 




J • 


13,000 




10-14 






7000 




15-16 


35 


10-14 






28 






8000 


2800 


8-13 


5 




5500 


1500 


22 






6400 


2200 


1 1-23 






4500-6000 


I700 


15-26 






6000 


24OO 


2-3 










7-10 






5500 




0.9 


3 




1000 




3-7 


4 


1 


800 




H-3+ 


2i 




600 




4 






950 




4-7 


2-4 


i 


750 




4-6 


4 








4-7 


3i 

2£-5 

i£-3 
i-6 




650 





From Vol. XXII., Encyc. Britannica. 



7^ 2 EXPERIMENTAL ENGINEERING. 

VII. 

STRENGTH OF METALS AT DIFFERENT TEMPERATURES. 

[Experiments of A. Le Chatelier, Paris, 1891.] 

Cast-brass. 
Strength remains about constant until 500° C. 



Temperature 

Centigrade. 

Deg. 


Breaking-load 

per Square Inch. 

Lbs. 


Elongation. 
Per Cent. 


15 
155 
230 
480 
540 
690 


19,457 
17,864 
17,508 

17,693 

11,677 

5,66o 


O.24 

O.71 

0.35 
O.89 

0.54 
O.71 

, 



Tin-bronze. 



Temperature 

Centigrade. 

Deg. 


Breaking-load 

per Square Inch. 

Lbs. 


Elongation. 
Per Cent. 


Duration of Test. 


15 
140 
230 
250 
300 
350 
415 


22,614 

23,582 
20.524 

18,717 
17,124 

15,574 
9,03! 


5-7 
7.08 

3-9 
4.28 
2.0 
1.4 


M. S. 
8 30 

5 30 

6 30 
21 
17 
16 

2 30 



Aluminium-brass. 



Temperature 

Centigrade. 

Deg. 


Breaking-load 

per Square Inch. 

Lbs. 


Elongation in 5.502 

Inches. 

Per Cent. 


15 
140 
230 
320 


49, l8 3 
46,168 
42,100 
30,380 


30.7 [ 

37-o 

33-2 f 



IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES. 783 

VIII. 
IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES. 



Meta\s from 32 to 212 

Aluminium 

Antimony 

Bismuth ......... 

Brass 

Copper 

Iron, cast 

Iron, wrought 

Gold 

Lead 

Mercury at 32 . .. 

Nickel 

Platinum... 

Silver. 

Steel 

Tin 

Zinc 

Stones — 

Chalk 

Limestone 

Mascnry 

Marble, gray 

Marble, white. .. . 

Woods — 

Oak 

Pine, white 

Mineral substances — 

Charcoal, pine 

Coal, anthracite. . 

Coke 

Glass, white 

Sulphur 

Liquids- 
Alcohol, mean. ... 

Oil, petroleum 

Steam at 212 

Turpentine.... . .. 

Water at 62° 

Solid- 
Ice at 32 

Gases — 

Air at 32 

Oxygen 

Hydrogen 

Carbonic acid 



Specific 
Gravity. 
Water, 1. 



61 to 2.65 
6.712 

9.823 

8.1 

8.788 

7-5 

7-744 
19-258 
"•352 
13.598 

8.800 
16.000 
10.474 

7-834 
7.291 
7. 191 



.784 
.156 
.240 
.686 
.650 

.86 
•55 



0006 

87 

000 



.00127 

.000089 

.00198 



Specific 
Heat. 

Water, 1 



.212 

0508 

0308 

oy39 

092 

1298 

1138 

0324 

03 r 4 

0333 

1086 

0324 

056 

1165 

0562 

0953 



.2149 
.2174 



.2694 
.2158 



.2415 

.2411 

.203 

.1977 

.2026 



6588 
3 1 
847 
416 



.238 
.2412 

3-2936 
.2210 



Absorbing 
and Radiat- 
ing Power of 

Bodies in 
Units of Heat 

per Square 
Foot for Dif- 
ference of 1°. 



.049 

.0327 
.648 

.566 

.1329 



.0265 



.0439 
.049 



.6786 

•735 

•735 

•735 

•735 



.5948 



1.0853 



Conducting 




Power in 




Units of Heat 


Weight 


per Square 


in 


Foot of Sur- 


Pounds 


face with 




Difference 




of 1°. 






Per 




cu. in. 




O.IIOO 




0.2428 




0-3533 




0.2930 


S*S-o 


0.3179 


233.0 


0.2707 


233.0 


0.2801 




. 6965 


113.0 


0.4106 




0.4918 




0.3183 




0.5787 




0.3788 




0.2916 




0.2637 


225.0 


0.26 




Per 




cu. ft. 




174.0 





197.0 




140.0 


28.0 


168.0 


22.4 


165.0 


i-7 


54-o 


.748 


34-6 




27-5 




88.7 




62.5 


6.6 


180.7 




127.0 




57-5 




55-o 




• 050 




54-37 




62.35 




57-5 




.0807 




.0892 




•°o559 




.1234 



Melting 

Points. 

Degrees 

Fahr. 



810 
476 

1692 

1996 

2250 

2900 

2590 

608 

—39 

2640 

3700 

2000 

4000 

446 

680 



See also pages 338 and 383. 



784 



EXPERIMEN TA L ENGINEERING. 



IX. — COEFFICIENTS OF FRICTION. (Morin.) (Page I9 6.> 



No. 



Surfaces. 



Wood on wood, dry. 

" " " soaked 

Metals on oak, dry 

" " " wet 

" " " soapy \ 

" " elm, dry 

Hemp on oak, " 

** " " wet 

Leather on oak . 

Leather on metals, dry 

" " " wet 

" " " greasy 

" " " oily 

Metals on metals, dry 

44 44 4< wet.. 

Smooth surfaces, occasionally 

greased 

Smooth surfaces, continually 

greased 

Smooth surfaces, best results. . . . 
Bronze on lignum vitse, wet. . . . 



Angle of 
Repose. 



Deg 

14 to 26I 
III to 2 
26I to 31 
13I to 14-i 

"1 

ill to 14 

28 

1 8* 

15 to 19I 
29I 

20 

13 
81 
81 to ill 
16I 

4 to 4I 

3 
if to 2 

3? 



Coefficient of 
Friction. 



J = tan <£ 



0.25 to .5 

.2 to .04 
.5 to .6 
. 24 to . 26 

.2 
.2 tO .25 

•53 
•33 
.27 to .38 
.56 
•36 
•23 
• 15 

.15 to .2 

•3 

.07 to .08 

.05 
.03 to .036 

.05? 



+f 



4 to 2 

5 to 25 

2 tO 1 67 
4.17 10 3.85 

5 
5 to 4 
1.89 

3 
3.7 to 2 . 86 

1.79 
2.78 

4-35 

6.67 

6.67 to 5 

3-33 

14.3 to 12.5 



33-3 



20 

to 27.O 

20? 



Note.— The above table is defective since the pressure per square inch is not given. The 
coefficient of friction diminishes with increase of pressure, so that in some k cases the total friction 
remains constant- 



X. — HYPERBOLIC OR NAPERIAN LOGARITHMS. 



N. 


Log. 


N. 


Log. 


N. I 


.og. 


N. 


Log. 


N. 


Log. 


x.oo 


0.0000 


2.30 


0.8329 


3.60 1 


2809 


4.90 


1.5892 


6.40 


18563 


1.05 


0.0488 


2-35 


0.8544 


3-65 1 


2947 


4-95 


1-5994 


6.50 


1. 8718 


X.IO 


0-0953 


2.40 


0.8755 


3-7o 1 


3083 


500 


1 


6094 


6.60 


1. 8871 


LIS 


0.1398 


2-45 


0.8961 


3-75 1 


3218 


5-05 


1 


6194 


6.70 


I.902t 


X.20 


0.1823 


2.50 


0.9163 


3.80 1 


3350 


5.10 


1 


6292 


6.80 


I. 9169 


1. 25 


0.2231 


2-55 


09361 


3-85 


3481 


5-i5 


1 


6390 


6.90 


1-9315 


J. 30 


0.2624 


2.60 


o.9555 


3.90 1 


3610 


5.20 


1 


6487 


7.00 


1-9459 


1-35 


0.3001 


2.65 


0.9746 


3-95 1 


3737 


5-25 


1 


6582 


7.20 


1. 9741 


x-4° 


0.3365 


2.70 


o-9933 


4.00 1 


386.3 


5-3o 


1 


6677 


7.40 


2.0015 


*-45 


0.3716 


2-75 


1.0116 


4.05 1 


3987 


5-S5 


X 


6771 


7.60 


2.0281 


1.50 


0.4055 


2.80 


1.0296 


4.10 1 


4110 


5-40 


1 


6864 


7.80 


2.0541 


1-55 


0.4383 


2.85 


i-»473 


4-^5 1 


4 2 3i 


5-45 


1 


6956 


8.00 


2.0794 


X.60 


0.4700 


2.90 


1.0647 


4.20 1 


435* 


5-5o 


1 


7047 


8.25 


2.1102 


J- 65 


0.5008 


2-95 


1. 0818 


4.25 1 


4469 


5-55 


1 


7138 


8.50 


2 . 1401 


I.70 


0.5306 


3-oo 


1 .0986 


4-3° * 


4586 


5- 60 


1 


7228 


8.75 


2 . 1691 


1-75 


0.5596 


3-05 


i-"54 


4-35 1 


4701 


5-6 5 


1 


73i7 


9.00 


2.1972 


x.80 


0.5878 


3.10 


1.1314 


4.40 1 


4816 


5-7o 


1 


7405 


925 


2.2246 


I.85 


0.6152 


3-i5 


1. 1474 


4-45 1 


4929 


5-75 


x 


7492 


950 


2.2513 


I.90 


0.6419 


3.20 


1.1632 


4.50 1 


5041 


5.80 


1 


7579 


9-75 


2 • 2773 


i-95 


0.6678 


3-25 


1. 1787 


4-55 1 


5151 


5-85 


1 


7664 


10.00 


2 . 3026 


2.00 


0.6931 


3-3o 


I-J939 


4.60 1 


5261 


5-90 


1 


775o 


11.00 


2-3979 


2.05 


0.7178 


3-35 


1.2090 


4.65 1 


5369 


5 95 


1 


7834 


12.00 


2.4849 


2. IO 


0.7419 


3 40 


1.2238 


4.70 1 


5476 


6.00 


1 


7918 


13.00 


2 5649 


2.15 


0.7655 


3-45 


T.2384 


4-75 1 


SS81 


6.10 


1 


8083 


14.00 


2.6391 


2.20 


0.7885 


3 5o 


1.2528 


4 80 1 


5686 


6.20 


1 


8245 


15.00 


2.7081 


a. 25 


0.8109 


355 


1.2669 


4.85 X 


579<5 


6.30 


1.8405 


16.00 


2 . 7726 



MOISTURE ABSORBED BY THE AIR— HUMIDITY, 785 



XL 

MOISTURE ABSORBED BY AIR.* 

The Quantity of Water which Air is Capable of Absorbing to THE 

Point of Maximum Saturation, in Grains per Cubic Foot 

for Various Temperatures. 



Degrees 


Grains in a 


Degrees 


Grains in a 


Fahr. 


Cubic Foot. 


Fahr. 


Cubic Foot. 


— 20 


O.219 


55 


4.849 


— IO 


0.356 


57 


5- 191 


- 5 


O.450 


60 


5-744 





O.564 


62 


6.142 


5 


O.705 


65 


6.782 


10 


O.873 


67 


7.24I 


15 


I.075 


70 


7.98o 


20 


1. 321 


72 


8.508 


25 


1. 6ll 


75 


9-356 


30 


I.958 


77 


9.961 


32 


2. 113 


80 


10.933 


35 


2.366 


85 


12.736 


40 


2.849 


90 


14.791 


45 


3-414 


95 


17.124 


50 


4.O76 


100 


19.766 


52 


4.372 


105 


22.751 



XII. 

RELATIVE HUMIDITY OF THE AIR.* 



Difference of 

Temperature, 

Wet and Dry 

Bulb. 


Temperature of the Air. 


32° F. 


70° F. 


90 F. 


0.5 

I 
2 

3 
4 
5 
6 

7 

8 

9 
10 
12 
14 

16 
18 
20 
22 
24 


95 
90 

79 
69 
59 
50 
40 
3i 
21 
12 
3 


98 
95 
90 
86 
81 
77 
72 
68 
64 
60 
55 
48 
40 
33 
26 

19 
13 

7 


98 
96 
92 

88 

85 
81 
78 
75 
71 
68 

65 
59 
53 
47 
41 
36 
32 
26 















♦From Weather Bulletin No. 127, U. S. Dept. of Agriculture, 1897, faf 
barometer 92.4 



7 86 



EXPERIMENTAL ENGINEERING. 



xni. 

(Page 202.) 
TABLE OF BEAUME'S HYDROMETER SCALE WITH CORRE- 
SPONDING SPECIFIC GRAVITIES. 

For Liquids Lighter than Water. Temp. 6o° Fahr. 



Beaume. 


Specific 


Beaume* . 


Specific 


Beaume^ 


Specific 




Specific 




Gravity. 




Gravity. 




Gravity. 




Gravity. 


10 


I. OOOO 


31 


O.8695 


52 


O.7692 


73 


O.6896 


II 


O.9929 


32 


0.8641 


53 


O.7650 


74 


O.6863 


12 


O.9859 


33 


O.8588 


54 


O.7608 


75 


O.6829 


13 


O.9790 


34 


O.8536 


55 


O.7567 


76 


O.6796 


14 


O.9722 


35 


O.8484 


56 


O.7526 


77 


O.6763 


15 


O.9655 


36 


O.8433 


57 


O.7486 


78 


O.673O 


16 


O.9589 


37 


O.8383 


58 


O.7446 


79 


O.6698 


17 


O.9523 


38 


O.8333 


59 


O.7407 


80 


O.6666 


18 


O.9459 


39 


O.8284 


60 


0.7368 


81 


O.6635 


19 


0.9395 


40 


O.8235 


61 


O.7329 


82 


O.6604 


20 


0.9333 


4i 


O.8187 


62 


O.729O 


83 


O.6573 


21 


O.9271 


42 


O.8139 


63 


0.7253 


84 


O.6542 


22 


O.9210 


43 


O.8092 


64 


O.7216 


85 


O.6511 


23 


O.9150 


44 


O.8045 


65 


0.7I79 


86 


O.6481 


24 


O.909O 


45 


O.8000 


66 


O.7142 


87 


O.6451 


25 


O.9032 


46 


0.7954 


67 


O.7106 


88 


O.6422 


*6 


O.8974 


47 


O.7909 


68 


O.7070 


89 


O.6392 


?7 


O.8917 


48 


O.7865 


69 


0.7035 


90 


O.6363 


?8 


O.8860 


49 


O.7821 


7o 


O. 7000 






29 


O.8805 


50 


O.7777 


7i 


0.6965 






1o 


O.8750 


5i 


0.7734 


72 


O.6930 







For Liquids Heavier than Water. 


Temp. 6o° 


Fahr. 




Beau»ne". 


Specific 


Beaume. 


Specific 


Beaume\ 


Specific 


Beaume\ 


Specific 




Gravity. 




Gravity. 




Gravity. 




Gravity. 


I 


I.0069 


19 


1. 1507 


37 


1.3425 


55 


I.6III 


2 


I. OI39 


20 


1. 1600 


38 


1 


3551 


56 


I.6292 


3 


1. 02 1 1 


21 


1. 1693 


39 


1 


3679 


57 


I.6477 


4 


I.0283 


22 


1. 1788 


40 


I 


3809 


58 


1. 1666 


5 


I.0357 


23 


1. 1885 


4i 


I 


3942 


59 


I.6860 


6 


1. 0431 


24 


I.I983 


42 


I 


4077 


60 


I.7056 


7 


I.0507 


25 


I.2083 


43 


I 


4215 


61 


1. 7261 


8 


I.0583 


26 


1. 2184 


44 


I 


4356 


62 


I.7469 


9 


1. 0661 


27 


1.2288 


45 


I 


4500 


63 


I.7682 


10 


I.0740 


28 


1.2393 


46 


I 


4646 


64 


1. 790I 


11 


I.0820 


29 


I.2500 


47 


1 


4795 


65 


1. 8125 


12 


I.O902 


30 


I.2608 


48 


1 


4949 


66 


1.8354 


13 


I.0984 


31 


1. 2719 


49 


I 


5104 


67 


I.8589 


14 


1. 1068 


32 


1. 2831 


50 


I 


5263 


68 


1. 8831 


15 


I.II53 


33 


I.2946 


5i 


1 


5425 


69 


1.9079 


16 


1. 1 240 


34 


I.3063 


52 


I 


5591 


7o 


1-9333 


17 


1. 1328 


35 


I.3181 


53 


I 


576o 






18 


I.1417 


36 


I.3302 


54 


1.5934 




. 



COMPOSITION OF VARIOUS FUELS OF U. S. 787 

XIV. 

COMPOSITION OF VARIOUS FUELS OF THE UNITED STATES. 



Mine or Name. 



Mount Pleasant 

Exeter (Rice) 

Exeter 

Coxe's No. 1. 

No. 11 Forty-foot. .. 
York Farm (Bkwt).. 

Jermyn 

Cayuga 

Manville Shalt 

Avondale 

Oxford 

Continental 

Woodward' 

Cumberland 

Eureka 

Antrim 

Long Valley 

New River 

Pocahontas 

Cardiff 

Union 

New Castle (Lump). 
Mt. Olive (Lump)... 

Big Muddy 

Streator (Lump) 

Gillespie 

Ladd (Lump) 

Wilmington (Lump). 

Indiana Block 

New Pittsburgh 

Vanderpoo! (Lump). 

Wills Creek 

Jackson Hiil. 

Hocking Valley 

Brier Hiil 

Weilsville 

Goshen 

Hastings 

Turtie Creek . .. 

"Voughiogheny 

Trotter 

Reynoldsville 

Pittsburgh 

Summer Hill (Slack) 

Monongahela 

Leisenring 

CanneH.... 

Cooperstown 



Locality. 



Scranton, Pa. 
Pittston, Pa.. 



Scranton, Pa., Slate 
out.... . 

Scranton. Pa 

Schuylkill Co., Pa. 

Pottsviiie, Pa 

Scranton, Pa 



Maryland 

Pennsylvania 



Towanda. Pa . 
West Virginia. 



Wales. 



Jerome Park, Colo. 
New Castle, Colo.. . 
Illinois 



Streator, 111 . 
Illinois 



Wilmington. 111. 
Brazil, Ind. 
Indiana Block .. 

Kentucky... 

Ohio ..... 



Nebraska 

Monongahela R.,Pa. 

Pennsylvania . 

Connellsville.Pa. . . 
Pennsylvania 



Monongahela R.. Pa 

Connellsville. Pa 

Peyton. W. Va 

Nova Scotia 







Coal as Received. 
















B.T.U. 

per lb. 












Fixed 
C. 


Vol. 
Matter. 


Ash. 


Water 


B.T.U. 


Comb. 


80.54 


7-54 


10.65 


127 


12.307 


1.3-973 


79-41 


8.16 


12.18 


•25 


12,400 


14160 


74 73 


5-7 1 


18.90 


.66 


11.360 


14.122 


87.96 


2.50 


6.77 


2.97 


13-324 


14 760 


83 


98 


4.99 


9 91 


I. 12 


12,903 


14503 


7S 


29 


5-47 


18.43 


.81 


11,430 


14.152 


81 


6b 


5-78 


10.84 


I.70 


12,036 


13.760 


84 


46 


5 37 


9.20 


97 


12,294 


13.684 


bs 


70 


5-95 


7 3 1 


1.04 


12.934 


14.120 


86 


68 


5-89 


b.15 


1.28 


13.051 


14.095 


9t 


45 


5-°3 


2.17 


1 35 


13-254 


13.736 


83 


'3 


5-98 


9 62 


1.27 


12.943 


M.525 


79 23 


3 73 


13 7 r 


3 33 


12,149 


14.642 


75 So 


17.00 


6 00 


1 5o 


14.700 


15,900 


7° 47 


23.86 


4.87 


.80 


14.195 


15.046 


69 30 


18.57 


10'. 90 


1.23 


13,528 


15.397 


67.32 


25.01 


11 .12 


1-55 


12,965 


14.845 


72.90 


20.42 


5.00 


1.18 


m.200 


16200 


68.88 


21.81 


6.75 


2.56 


14.580 


16.070 


67'45 


20.41 


" 33 


.81 


12.789 


14-555 


52.86 


36.70 


8.44 


2.00 


13.650 


15.240 


50.80 


35.8o 


10 90 


2.50 


11,900 


13.750 


44.10 


33 10 


14.70 


8.10 


10.600 


13.730 


53.80 


30.70 


8.00 


7-5° 


12.400 


14-675 


44 30 


36 35 


11 -40 


7-95 


n. 600 


14,380 


49 55 


39-94 


11.74 


3-77 


10.506 


12.425 


42.45 


3230 


13.25 


12.00 


10.900 


14-583 


39-9° 


32 . 80 


11 .80 


15.50 


10.200 


14.030 


53 70 


30.60 


11.00 


9.70 


11,300 


14.250 


40.40 


42.23 


11.48 


5 89 


11.546 


13-97? 


54.60 


34.10 


7-30 


4.00 


12.800 


14.430 


46. C 5 


36.23 


n.63 


5 49 


T2.060 


14-550 


55.50 


30.72 


10. 90 


2 88 


11 .800 


13,685 


48 90 


36.3c 


8 30 


6.50 


12.C12 


14,100 


56 30 


34.. 60 


4-3o 


4.80 


12.900 


14.200 


49-5? 


33 50 


15.50 


i-45 


12.400 


I4.930 


49 83 


',8.03 


6 91 


5 23 


11.966 


13.619 


60.88 


27,82 


11.09 


21 


12.935 


14.583 


59-45 


34.22 


4.22 


2 11 


14.150 


15.107 


54.00 


32.25 


12-50 


1.25 


12.900 


14.958 


58 90 


28. 27 


9 «3 


3.00 


12.539 


14,386 


59.04 


30.77 


9.16 


1 07. 


i4^4 2 


15.746 


S3 3o 


34.60 


9.70 


2.4c 


12,400 


14.107 


«> 60 


33.00 


1 3 40 


3 00 


12.750 


15.250 


58.61 


31,29 


7 83 


2.27 


13.126 


14.600 


63 .56 


28.71 


6 10 


1.93 


15,005 


16,313 


4T 32 


42.84 


15.36 


.48 


12.224 


J 4-5 2 3 


64 44 


30.42 


4 03 


1. 11 


15,266 


16,091 



a 
p </> 

- 3 

J3 O 

a 

u 
c/i 



ANALYSES OF ASH, 





Specific 
Grav. 


Color 

of Ash. 


Silica. 


Alum- 
ina. 


Oxide 

Iron. 


Lime, 


Mag- 
nesia. 


Loss. 


Acids 
S.&P. 


Pennsylvania Anthracite 

" Bituminous 

Welsh Anthracite 


1-559 

1-372 

1.32 

1.26 

1.27 


Reddish 
Buff. 
Gray. 


45-6 
76.0 
40.0 
37-6 
19-3 


42.75 
21.00 
44-8 
52.0 
11. 6 


9.43 
2.60 

5-8' 


1. 41 

12.0 

3-7 
23-7 


o-33 

trace 
1.1 
2.6 

t 


0.48 
0.40 






2.97 


Lignite 


33-8 





< 
w 

O 
W 
H 

< 

> < 
x «« 

O 

w 

H 

CU 
C 

OS 



788 

ft 8 ?* 

flttP4fi 

♦JrtOs 
1* «3 

a-° «& 

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O rt w m 

3 <L> b 3 

2 * o J> 

•Ss* a 



•23 ffl 

8?S . 

c v a a 
cc 9 o 

w°£q 
.2 v ex 3 

c o^ 

:^° 

■S «iS s 

S2 83 
23 



&§ a 



EX PERI MEN TAL ENGINEERING. 



g<*88 
2 I'll 

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PROPERTIES OF SATURATED STEAM. 



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COCOCOCOCOCOCOPO 


•spunod 
ai 'txreajs jo }ooj oiqno b jo iqSia^\ 





1000 

ON ■*■ 
>- co u-> 
On m ro 

PJ P) P) 


m m ONNM3<mN0 M 
iflO \tO "*00 CO t-^ M VO 
VO 00 On O Pi CO lOVO 00 0> 
lO r-~ On CM -*VO 00 M T 
t-~ t>. r-00 00 00 00 On On On 


« 8 N mOS*0 
•♦OO Pi 10 On co t-v 

►" CM CO tovo NONO 
SOih COlOt-»ONPI 
OnOnOOOOOw 
pi P) cocococococo 








i 

D 

W 
P 
H 
55 

a 


•ootjBJodBAa jo si ran ui * z£ 
8AoqB uopBaodBAa jo jBaq ibjox 


k 


N -*VO 

P) PI PI 
CM 04 P) 


OOON •♦VO 00 O N CO lO 
t>.00 00000000 OnOOnOn 

NBNMNdCINdtl 
NCNMNINWMNCNICN" 


'Ota n 'j-vc 00 01 
o-onoooooo 
m pi cocococococo 

WNNN«N«M 








2 

"5 

a 

JZ 

H 

JS 

'*» 
'C 

CQ 

a 


Total heat of 
evaporation 
above 32 





f~ t>.vO 

ir> ir> 10 
00 00 00 


O ONN*ON COVO 00 On On 
lO CO « m ON00 VO ■*• M 

h mm t~.oo cn >*-vo 00 

vovovovovo (^t^f-.t^f-. 
oocooooooooooooooooo 


oovo -»*-0 ir> ov h CO 

OO VO -* P" ONVO ■* H 
On w CO lOVO 00 P> 

r^oo 06 00 00 00 o> o\ 

0000000000000000 








Latent heat of 
evaporation 
at pressure P 


^ 

s 

V 


lOONVD 
CO M t^ 

OMOO 

■*•<>• Tj- 

00 00 00 


VO 00 Ci ONOO 11 t*» WiVO 00 
M t-~ CO00 •*■ M t». ■*• n OO 

VO Hf t^CNOO Tj-ONiOMVO 

coconmhimOOOOn 
00000000000000000000 


com pi 100 t*.r-.c 
vo ■<*■ pi On t-vo vo 
pioo •♦O iom t^co 
00 00 00 r-. t-vvo vc 

VCVCVCVCVOVOVCVC 
00CV.COO0O0000000 


lis 





VO co 

CO "*■ Tf 


•*■ On COOO (HO Oh N * 

t-^C -«-C^W -fl-C^M Tj-t- 

•4- m \i*i invo vo vo t-~ t^. t- 


VO C^OO O M M PI M 

P~vO O COVO ON Pi 
000000 ONONONONO 








00 00 00 


OOOOOOOOOOOOOOCOOOOO 


ooooooooooooooco 


111 




ONVO r-» 
VO M VO 


M On O m VO tOOO ^- •* •*• 
»OVO 00 w COVO On CO t^ H 
MVO H t^M NNOO COON 


00 t Nt m o> m in 

lOQ «00 IflH fsCO 
*5 lOMC S NCI 


On On On 
t-« t-> t»» 


CN M M O O OnOO 00 t^ 
ON ON On ON OnOO 00 00 00 00 


t-~ (--vc vd 10 in ■*- tS- 
0CO0O00O0OCO003O 


Required to 

raise the 

temperature 

of the, water 

from 32* to T°. 


to 

u 




N M IT) 

ON '♦CO 
IO M 00 


■^•M VllOH M Oncocom 
M VO On N >0 t-»00 l- M 
1/]H C^^t"0NO W ONlOM 


loins iniopi -*co 

PIPiPiMOONf-iA 
(-.COOIOMVO NOO 


OHM 

co co co 


N CO CO ■<*■ lO lOVO VO t^co 
cococococococococoro 


OOOnO-OmmNPI 

MMMplNPIPJPJ 

COCOCOCOPOCOCOCO 


•sawSap ^laqasaq^ 'aamBjadmaj, 


•»>» 


VO O00 
t» ^ 


mOvooovomOvOOh 
00 O l-i N CO-^-^COCON 
VO COONIOM tstOOMflH 


xo p>c-.mm*ONH 
OOOVO »MCO •*■ * 
J^PiCO -<»-0 «OM t* 


ON M 
CO CO CO 


H N P) CO •* ■<»■ lO U-IVO C-. 

cococococococonjcoco 


t^OO CO ON M M 

cocococococococo 


•qoui axenbs aad 
spunod ui 'unuttBA e aAoqB sjnssaj j 


■*. 


00 On O 


M M CO •* «OVO t».0O On 
M««NN(MNPICNiCO 


M N CO * IOVO t^OO 
cocorocofOcococo 












PROPERTIES OF SATURATED STEAM. 



793 



*. 


aa 


w CM CO^WVO PVCO OnO 


NBRcggN8 


2 ro5-5,Ngooo8U»§°8U.8S»§S,8S8S,§ 

NNNN«NN«N<n ro-*-->l-in| mvO VO t>. P»00 00 ON On 




H M „„„„„„„„„„ ,„„„-., 


^ 


r» m 


N*K OMnrnM ov o COVO CO 00 


mscninooo Onpoooo 


Pv00 m 00 


vo mvo *vo m o ■»*■ o 


00 p» 

O O 


NO ■*■ CO PI O Onoo P».vo ■*■ 1 m^mNO 
On On On On OnOO OO CO 00 00 | P-«VO W rj- -f 


■*oo rooo "/Onion On m 
pocnipiihihooOOnon 


cm <m moo 
oo t^vo m 


momcM OP~*mM o 
m*-**mmmmmm 




l 




u 

ft 


CM M 

OO VO 


O OnOO 00 OO On h pi 
•n+ m OMOMm O 00 VO 

hmOOOOOOOO 


NO W mOO NO 

oo m onno m 
two ■*■ m cni 


*bnO» inoNCMnm vnt^pipi 
mvo r^ On n in on rooo ro 1 cm \o ■*• ->j- 
►- Onoo oo t^vo vo mm] ro m On 


oo h ovo p^mcM mo 
m o moo m ovo m o oo 
oo P^ r~vo vo m m m m ■*• 


co co 


rtn«Mffi«nnN pi 






it 

o 


•ooo 
m 

■o-vo 


m niin PvCO CO t^vo to CO 
t-» O CONO On P" >OO0 h •*■ 
•*VO t-^00 On m PI CO «OVO 

00 PI *vo OH niAN 
m N N « N « fOCOmf^ 
commrommmmcoco 


io»»oo 
oo r-» co m 
OO O PI pi to 
oo o m pi m 
moo on* 
m m ■* •*■ ■* 


mr^ONrOMNO O ■*• OvO 
ONroroO roPl ON Pi 
N Pi i- Ooovo rOMCOm 
■■*- mvo P- P-.00 On H 

vo oo o pi -<J-vo oo m mm 
•h/ tj- m m in m mvo vo vo 


■* mvo 
moo m o 
m m m p~ 

* P^ O M 

m m mvo 
P-00 o 


o vo m moo m m ■*••*■ en 

oooooooooooo 
m m c^ o m Tj-vo oo o cm 

VO VO VO VO P^ P^ C-, P^CO 00 

m pi ro * mvo t^oo o o 










" 


MHHHMMHMWf, 


to 


*. ro 

m co 
CM CM 


iovo ooo»n -*vo oo o 
HxHcmaocttin 


nOhio O * 
•*VO NONO 

cirtmfn + 
pi pi pi pi pi 


NO « ■* mvO NNNS 
b ro* mvo P-.CO o- <-> 
■***-<t-'«-'*'**mm 

PIPIPIPICMPIJIPICMPI 


vo * P- 
mvo vo vo 
CM CM CM CM 


O mvO O CM iriNOM CO 
P~ P-. P~ P^OO 00 CO 00 O ON 














* 


00 in 


■♦pi o>«no *noo o 
pi o in cm cjixih t-^ * o 
t^oo o « «im t^co o is 


M M M « ON 

(O lONnim 
nnno O n 


N O O m On mvo O vo 00 
ONMOowOt^o-oom 
moo ON-pipimmpipi 


* 0_ cw 


00000 O *0 m0V3 
vo * m p^ o m mvo p^vo 


15 

< 


O On 
00 lO 


OOOOOOOOmm 
0000 OnOnOnOnOnOnOnOn 


pi -<f in P-oo 

On On On On On 


on o « m -■*• mvo tvOO o 

oooooooooo 
hcinnnnnnnci 


m n m * 

M m CN) CM 
C* CM CM PI 


t>. O m moo O CM -tf-vo 00 
p» romrom-N*-*'"!-*-* 
CMCMCMPICMCMCMCMCMN 


.. 












o 


»0 CM 
ID lO 

On m 


m w ■*• P-.VO t-» o vo ■*■ 
in in '-ono no t-^oo o m n 
ih smoiOH r~- * o vo 


cm on m m m 
m invo t- 
On en On p- m 


vo cm oo m Onvo w m On m 
m*CNi o moo NO O 
mvo oo w *oo * onvo m 


°3-omo 


VOVO OO0CM ■*« O'O 

■*• cm vo m m *oo vo ■*• ro 


m m 

NO O 
Ol> CO 


in ->J- * m m m cm n o) H 

nOnOnOnOnOnOnOnONCnO 
00000000000000000000 


NNtO N't 

mmmt-t 
00 00 oo 00 00 


moo mmo Nino 000 
rj-mmmmcM cm cm cm m 

00000000000000000000 


N N O M 

o ooo 00 
00 t^ l> o 


mvo orot~.M mo mo 
p~.vo mm*"*-mmcM cm 

P.NNP.NSP.P.P.P. 


O 


O ON00 no -<S- >-i O P» •* N On 
lOOO 1 CONO O CM * P** m in 
OO MMMMPICMCMrOrOrO 


vo *(< mo 
« mN r-vNO 

NO CO PI ■* 


oo vo mvo oo m w m 
•*• O vo m moo « pi m m 

VO 00 Ob PnT m mvo t^OO 


PJ NO 00 


CM 00 O -*00 O m 00 

M M N M m O OOO VO 


CM PI NNNNNNNCINN 
COCO |O000000000O000CO0000 


PI PI COflfO 
CO CO CO CO 00 


mmm-j-*-H-Ti--<i-** 

00 00 00 oo 00 00 CO 00 OO 00 


m m mNO 

00 00 00 00 


vo vo vo vo vo vo vo ininin 

OOCOOOOOOOOOOOOOOOOO 


•s 
tH 

o 

a 


Hid h moo vo vo t>. o vo Tt- in 

OS * m 00 VO -*• PI M ONCO P^ 
GN ■*■ 0^O m N^OiioOnO tl 


vo m m o w 

O- On ro IH 

pi moo •* n 


vo * cm oo moo i-i O oo 
f mvo co O O m r^ r-» 

ooo oo o« moo moo -i- 


Tt-00 M 

« m« o 


*oo o m ^-^-^-m ooo 
m o -*■ m o moo c^vo >o 


ro ro 1 cocmpimmoOOOO 
COOT) 00 00 CO OO 00 OO CO OO NN 

t^t^l p»p*p~p~p~p~c--p~p>p~ 


inn snj-m 

t^ PvVO NO NO 

t-» t-» r-~ r- t^ 


r~*>-oovo mooo mm 
inmm*'<j-**mmm 
t-^r-.r^p-p~t-.r~c-~t-~p~ 


N « co m l p^0mp»MinO'>s-O'«- 
cm m o o , oo oo pvvo no vo ■*• ■*• m m 
r» N P^vo 1 vo vo VO vo vo vo vo vo VO VO 


* 


On CO 

*8 


«im mm moo o< -*vo 

t^ "*• VO PI NMNNNO 

tow p^ cm co mon + o in 


PI 00 OnVO 
in OnO in vo 

O0O0 NON 


moo cmoo O t^mpxt^m 
•Hrvo mO mt^O mt>.m 
O m m o p~ m o mvo o 


1 

vovooon *N» ovoco* mo 
cm r- - in m o) m -too oo vo m ro 


co -*■ 
CM CM 

CO co 


* IT) invO NO P-« t^OO 0> On 
MNNONNCn'NMini 


* On * On CO 

ro ro •* ■*■ in 
ro ro ro ro ro 


co cmvo mr^o -<t-t-.o 
mvo O NN P^CO 00 30 o 
rorommmmmmmm 


vo o cm m- 1 ■<j-*mcvi6o6vo'*rMOO 

m m * mvo t>.00 O O O m CM CM 

1 


■>* 


t~» CM 
CM CO 

CM N 
in in 

CO m 


OxOOMNONOONn 
00 ONNnO rOVO On W 

co^O in m vo mnO pi 


vjIvOnO pi no 
■* PI CO in ro 
ro PI 00 rovo 


ovo un m m moo o m 
m ro p^co oo p^ m * m p» 
Np-incioo pop^o cm m 


VO CM CM N 

o ovo -vr 


O VO 00 *VO CM CM vo CM 

moo vo w o vo oo vo moo 


ro co ■«* in invd vo r^. t^co 

m in m m io in io io m in 


rooo N Si- 
vovo N r-~oo 
ro ro ro' ro ro 


momi^O Tj-r~M -*p^ 

OOOOOOOOOmmm 

mmmm*'*'<r-><-*-<t 


M '♦VO P^ 

ro * mvo 


two m ■<»• cm ovo m o vo 
p^oo oOMMMm** 
Tj-Tf-Nj-mmmmmmm 


■*, 


v>0 
CO'* 
H M 


M M n* vivo tvOO On 

HMHHHHMMHH 


O 

VO P»00 On 


oooooooooo 
m ci m * mvo pnoo o o 
ciciCiCincincMCMro 


m o m o 
m-«r ■♦m 


OOOOOOOOOO; 
mo mo mo mo moi 
mvo vo o ooa ao oi o o 



794 



EXPERIMENTAL ENGINEERING. 



XVI. 

ENTROPY OF WATER AND STEAM, 



Absolute 


Entropy per Pound. B.T.U. 


Absolute 


Entropy per Pound. 


B.T.U. 


Pressure, 






Pressure, 






Pounds per 




1 


Pounds per 






Square Inch. 


Water. 


Steam. 


Square Inch. 


Water. Steam. 


I 


0.134 


1.987 


IJ 5 


. 490 1 


•586 


2 


0-175 


1 


.924 


120 


O.494 1 


•583 


3 


O.201 


1 


.887 


I2 5 


O . 498 1 


.580 


4 


0.220 


1 


.861 


130 


O.501 1 


•577 


5 


°- 2 35 


I 


.841 


i35 


O-505 1 


•574 


6 


0.247 


I 


.825 


140 


0.508 1 


•57i 


7 


0.257 


I 


814 


i45 


0.512 1 


569 


8 


0.268 


I 


800 


J 5o 


o.5 J 5 1 


566 


9 


0.277 


1 


79° 


155 


0.518 1 


•563 


IO 


0.285 


I 


781 


160 


0.521 1 


561 


15 


°-3*S 


1 


747 


165 


0.524 1 


559 


20 


0.338 


I 


722 


170 


0.527 1 


•557 


25 


o-356 


I 


704 


175 


0.530 1 


555 


30 


0.370 


I 


689 


180 


0-533 1 


552 


35 


0.384 


I 


677 


185 


0.536 1 


55o 


40 


0-395 


I 


666 


190 


0-539 1 


548 


45 


0.405 


1 


657 


195 


0.542 1 


54& 


5° 


0-415 


I 


649 


200 


o.544 1 


545 


55 


0.423 


I 


641 


205 


o.547 1 


543 


60 


0.431 


I 


634 


210 


o.549 1 


54i 


65 


0.438 


I 


628 


215 


0-551 1 


540 


70 


0.444 


1 


623 


220 


0-554 1 


538 


75 


0.450 


1 


617* 


230 


0-559 1 


535 


80 


o.455 


I 


612 


240 


0.563 1 


532 


85 


0.461 


1 


608 


250 


0.567 1 


529 


90 


0.466 


1 


604 


260 


0.571 1. 


526 


95 


0.476 


1 


596 


270 


o.575 1 


523 


100 


0.480 


I 


593 


280 


o.579 I- 


520 


105 


0.482 


1 


593 


290 


0.583 1. 


5i8 


no 


0.485 


I 


59° 


300 


0.587 1. 


5i5 



DISCHARGE OF STEAM. 



79$ 



XVII. (Page 302.) 

DISCHARGE OF STEAM IN POUNDS PER HOUR CALCULATED 
BY NAPIER'S FORMULA. 







Pounds of Steam 




Absolute 
Pressure. 














Pounds. 


Diameter of 


Diameter of 


Diameter of 




Orifice ^ inch. 


Orifice ^ inch. 


Orifice £ inch. 


I 


O.039 


O.158 


O.631 


2 


O.079 


0.3:6 


I.262 


3 


0.II8 


0.473 


I.893 


4 


O.158 


O.631 


2.524 


5 


O.197 


O.789 


3-155 


6 


O.237 


0-947 


3.786 


7 


O.276 


1. 104 


4.417 


8 


0.315 


I.262 


5.048 


9 


0.354 


I.420 


5.680 


10 


0.395 


1.578 


6.3IT 


20 


O.789 


3.155 


12.622 


30 


1. 183 


4-733 


18.937 


40 


1.578 


6. 311 


25.244 


50 


I.972 


7.880 


3I-556 


60 


2.367 


9.467 


37.867 


70 


2.761 


n.045 


44.178 


80 


3-I56 


12.623 


50.488 


90 


3-55Q 


14.200 


=6. 800 


100 


3-947 


I5.778 


63-115 



XVIII. Page 4 2o.) 

PER CENT OF WATER AND STEAM EXHAUSTING INTO 

ATMOSPHERE.— BY THROTTLING CALORIMETER. 

(Per cent of moisture.) 



Tempt, in 
Calorimeter. 



Degrees Fahr. 



215 
220 
225 
230 
235 
240 
245 
250 

255 
260 
265 
270 
275 
280 
285 



Diff. i° Fahr 



Gauge-pressure on Main Steam-pipe. 



.0233 

.0207 

.0181 

.0154 

.0128 

.0102 

.0076 

.0049 

.0023 

.0005 — 

.0030— 

.0057- 

.0083— 

.0109 — 

.0136— 



.00052 



•0253 

.0227 

.0201 

■ 0173 

.0147 

.0122 

.0095 

.0069 

.0042 

.0016 

.0010- 

.0037- 

.0063- 



.00052 



0271 

0245 

0218 

0192 

0165 

0139 

0112 

0086 

0059 

0033 

0006 

0026 — 

0047— 

0073— 

0100 — 



.00053 



.0290 

.0263 

.0237 

.0210 

.0184 

•0157 

.0130 

.0104 

.0077 

.0051 

.0024 

.0002— 

.0029— 

.0056— 

.0082 — 



.00053 



.0307 

.0280 

•0253 

.0227 

.0200 

• 0173 

.0147 

.0120 

.0093 

.0066 

.0040 

.0013 

.0013- 

.0040- 

.0067- 



.00053 



65 



0322 

0296 

0269 

0242 

0215 

0189 

0162 

0135 

0108 

0081 

0055 

0028 

0001 

0026- 

0053- 



.00054 



•0338 

.0311 

.0284 

.0257 

.0230 

.0204 

.0177 

.0150 

.0123 

.0096 

.0069 

.0042 

.0015 

.0011 — 

.0038— 



.00054 



•o354 
.0327 
.0300 
.0273 
.0246 
.0219 
.0192 
.0165 
.0138 
.0111 
.0084 
.0057 
.0030 
.0003 
.0024- 



80 



0368 
0340 

0313 
0287 
0260 
0233 
0206 
0179 
0152 
0125 
0098 
0069 
0042 
0015 
ooia- 



00054 



■ oc, 054 



The minus sign indicates superheat. 

This amount divided by 0.48 and multiplied by the value of the latent hear uili give the 
degree of superheat. 




Diagram for Determining Per Cent of Moisture from Reading of Thermometer IN 
Throttling Calorimeter. (See text, page 425.) 

796 



ViCTOZS OF EVAPORATION. 



'97 



V) 

a 

K 

w 

E 

B. 
1/) 

O 

s 

h 
< 

2 

C 
z 
< 

w 

• X 

a 

X 
o. 
in 
O 

s 

I < 
5 

h 

H 
> 

C 
n 
< 

X 
y 
z 

w 

< 

o> 

t/J 

a 
w 

W 

s 

o 

(Li 

Z 
W 

as 

D 

(A 

u 

OS 

On 

W 


D 
< 


§ 


„ 




eensNK nnhnn »miomio 

CO rO CM CM M mOOO-OnCOOOCv tvVO 


O <f)0 >flOi 
vo m m Tf ro 


ro CM CM M M 


00 POOO fO r"N 

o o ov ooo 


« SB NCn 1 
00 N N'O vo 
o 


o 1 










P 


- 















00 


N 


On 

m 


vo m m o m n in O in o ^- On -<t- On ro 
mM«« m moo onoo oo t^ t-*vo vo 

CM CM CM CM CM CM CM CM M M m m M m M 


00 rooo ro r^ 
m in •*■<*■ ro 


CM fx CM t-. M 

rOCM CM M M 


vo m vo m in 

8 8 0*0*0 


O m o m o 
00 N r-~vo vo 



!J5 


H i 


£ 


(s, 


ro 
CM 


■«*■ 0- moo m 00 moo m (s CM N CM t-v ,M 
CO CM CM m m On OnOO 00 C-. NVO VO 


vo m vo m in 
m m •*■ ■+ cno 


O m o mo> 

ro CM CM m 


O On OnOO 00 


oo en rv moo 

c^ nvo no in 
O 


d 











H 


H 




















,„ 


CM 


hid uiO in in ■<»- On ■>!- o- -*oo 
mti tt - » ooo ooo n mo vo m 


ro ro rooo cm 
in •* tj- ro ro 


r«. CM t-» CM VO 

CM CM M M 


M VO M NO O 

ON OnOO 00 

m 


in o m o in 

n nvo vo in 
O 








o> 


H 




















00 


ro 


03 fflNN K N t-~ M N. m VO M VO M m 
CM CM m m O OOO 00 J-. C-VO VO IO 


m o m On 
in •>*■■* ro cm 


■>*■ On •*■ On ro 
CM m M O O 


00 rooo ro C-* 


N NO NM 

nvo no in m 
O 








- 



















t-- 


N 


•>*■ On moo ro oo moo rf)ts CM. N CM N m 
cm m m o o ooo oo t-. t^vo vo mio 

N » O tt K HMMMM MMHHH 


vo h vo h in 
tJ- tJ- ro ro CM 


m o »n on 

CM M M O ON 
M M M M O 


•* Ov -<t- On ro 
OOO 00 N N 
O O 


oo moo moo 
vo vo m m t 
O 





VO 


M 















Ov 





CM 
CM 


n\o o «io ino "io ■+ ovt)-ov -*oo 

CM M M On ON00 OO N \0 nO ul "1 >t 


rooo rooo cm 


NU f~ CM VO 

M M O OV 


MVO m vo 
OnOO 00 N c~- 
O O O O 


in O in o in 
vo vo in m t- 
O 




o 








VO 


M 

















ro 


CM 
CM 


O -^-oo moo moo rooo cm r-. CM t- CM vo 

11 m o O Ov Ooo oo nn vOO "im-* 


mvo wvo 
-1- ro ro cm cm 


inomoi- 

m m O On 


On ■*■ On -*00 

moo s nvo 
O 


vo m m -<r ■*• 



b' 















^ 


o 


IO m mo "i in m O * on » o> n 

M M On OnOO OO t-vVO OldlflNft 


flO rooo ro f-. 
cr, en CM CM m 


m O On On 


<o m vo m m 

COCO N NO 
O 


m o m o 
vo m m "1- -<r 
O 


b' 








* 



















so 





CM 


■*$• on moo ro oo moo en n Cn 1 no nh 

h o O OiO> ooco n r>.vo no uiinNj-Nt 


vo h vo m m 

ro ro CM cm m 


O m o m On 
h o ooo 


■«- On •<*■ On ro 

00 N NVO vo 




oo moo mca 
in in -<i- ii- ro 









* 


H 


a 


m 


CM 


m vo in O f WO ■+ o ■<*- O t)- ro 
mqOOOoooon t-.vo in io * * ro 


ro rooo CM 


t-» CM t» CM VO 

On OOO 


M vo M vo 
00 N MO vo 



in o m m 



o 1 








CO 




in 





CM 


On -"too moo rooo rooo CnI nc< cvNiO 
o onoo oo r-. c-^vo vo ioinNt^m 


mvo mvo O 
ro M CM m. m 


in m ■* 

2 2 8*o o 


On ■*• On tI-OO 

n nvo vo in 
O O O 


moo moo m 
ir> -t -t- en rn 



D j 








m 







N 




co mso n o rsN tsM io hio h in 
On Ovoo oo N r^vo vo in in -*■ ■<*■ m 


O in O m On 
ro cm cm m o 


Tf ON f On CO 
2 f?0^ O 


oo moo m n 
n txvo vo in 
O O O 


CM C-. CM N CM 

io ■*■ •* CO —, 












CM 


H 












1 


m 


m 


on 

8 


vo m io m OmOiOOv ■"a-ON-*ONro 
O on Onoo oo t^ rvvo m m •*■*>■ en m 


«?<2^ 


On OnOO 00 
m 


vo mvo m m 
n nvo vo in 
O 


io too 

lOfNtKim 



r 






- 




CM 









NO 

O 


rooo cmc~-cni t^CMt^CMvo mvomvoO 
On Onoo oo f». two vo io in -^- -^- ro ro 


m o m o *- 

CM CM M M o 


On t}- On Tf-00 
On Onoo oo r^ 
O O O 


moo moo cm 
nvo vo in in 
O 


Ml Nl( N 

Nftnmn 
O 


c 


CI 






H 


M 














in 
CM 


N 


o~ 


Mvoomo iriOmO'<*- Ov-^-On -*oo 
On Onoo oo t- c-^vo vo in ■* ^- ro ro CM 


rooo rooo cm 
cm m M o 


t^ CM tv CM VO 

On OnOO OO t-^ 
O O O O 


m vo m vo 
c-n.no vo in in 
O O 


io o io io 

NtNtnmci 
O 


o 








M 


M 


o c 

lis 

4) i w 

c « w 
- u 

41 [V. 




J 





vo ■<*- CM t~- io ro i-i mvo tci o Mn 


ro m oo vo ■st- 


cm o t^ in ro 


M 00 no tj- CM 


n io m m 


< 

CO 


11 •>!- f^ CM IO00 M rONO On <N IT) t-» 

iim mmcmcmcm CMrororo-^- 


rove 00 M Tf 

•«- -^- ■<*- m m 


NO n moo 
invo vo vo vo 


m mvo On cm 
n t- r-» noo 


in n o mvo 
00 oo o- o> o\ 


On 


fe 


m 


mOmOm omomo moiogio 

CO^-^inin NOVO t^ t>00 00 Ov On 


m o m o 
m M CM N ro 


>n o m m 

ro ■*■ -r m m 


m o m o 

IOnO N NOO 


in m o m 
00 ON Ov o O 




5 













7 9 8 



EXPERIMENTAL ENGINEERING. 



X 
XI 

6 

pa 

H 



w 

Q 

< z 

o 

I— I 

< w 



U 01 

X! CD 


X! 

~o£ 

u, CJ 

a 


oT'S 'S m2"m m ~£ OTMWWTO °ocoooooooi»ooooooc»oooooo 


Nominal 

Weight 

per 

Foot. 

Pounds. 


H O O lOOO -*oo ON ONO h m CM CM m o M IA00 UIh m 

-«- cm m co m no -a- o o mmo»o -<»- o no o o o no cm oo cm onh o o 
« -<*- IO00 HVO N«« MflOC oo m o cm m O ON OOO M 00 Pi 


HHCMCMCOIOOOOCM •*oo oooci ro d moo rOSNN <«) 
m h hi m cm cm ro-^Tj-T^-inirj-* u->no 


Length of 

Pipe 
Containing 

One 
Cubic Foot. 

Feet. 


tOVO H O Hi CM CO (ICO ON h K^-o OOO w 

MCI ^ ONio oh mmmo cm o ooo cm oo io cm o on ovo vo 


hco u>n ovo on o •*■ ro M M M 


K 

-8 

O td 

gl 

O o> 

►4 




IO »O00 HCO SinN OOO O ^-00 O CM O ONOO 00 CO CO M 
lOONcnmm ti-vo t^-^--^--<rt^Ti--4-LriO *nnoo ->l-Hioovo^-r<-)« 
hi *c-.hvovo t-~ roco uin o 000 t^vo in**mnmc) cm « w « 


Tj- C^>0 *m«NHHHH 


13 u 

c u -J 

v. ccj <u 
m<« <u 


insNN-t h oooo hi ino'tNSH mMnmanifloiflN 
■* Nm >t m o hi o w o»n -*vo oo t-^o Tama o>Mom« h 
■*■ vo in\o on ro "O m onoo t^vo lom'tmtonM cni n n n m 


ONt^lO-^CON N MM H HI 




to 

« 
w 

K 

W 
> 
in 

< 
K 

H 


3 5 


t-» o ro cni rv •*■ 

m -^-no on cm >noo r^ M-oo moN* tj-vo -*»o no •*■ m o> m ' 

N«VO ■* m ONO ONI^O * SNCnhcC (NOO ON o f^iome) tJ-VO 

O hi hi cm m ->j-\o oo t-^CMNO mno comoNmo on-^-ioo cm o ooo 


H H Ci B (OCI* tOVO 00 H CO tJ-VO O •*• U100 


ccj g 
C >— i 


m w ooo rONO 

t^-^-Hi ij-n-iCMNOOONO -*oo o hi oo 00 O rooo tv ir> 

m o> rONO on ro moo oo oo rovo Onoo m^mmrr ooo oo ■*•«»■ w 

O h h ro iooo *0 t»)N rooo t-> on onoo r~ c^oo O oo -4- cm vo 


wcMro-^-f-ONCMin onoo oo o moo iocinoiKh io 
m,m hi cm rnioW t-« On - comoo m ro 

M M M Hi cm CM 


1- 5 


on onoo t(-no oo ■* m cm h vo m- iono cm -<i-no m ■«• ooo m 

cm cm iri idno ionO mmONMvo coo t~-.NO cmnovo roc-^roMNOoo r~ 

hi cm ro moo nMco ■*■ rrvo lo onno ro -«-no tj- o o -*no c>no o>* 


h cm cni ->*-no on m fiott moo CM 00 O CONO m no •<*■ 
h h m ci ntiflNOiO ci mNO n m 

M H m m CM CM CM 




w 
u 
2 

a 
« 
[I] 
to 
§ 
& 
u 
PS 

u 


C M 


OO-tMNONCIinH-t rONO WOO N 0+ rovo NO t^OO NO 00 
-* ■*• in moo O cono o m ro it- -*no -^- iono r^r^t^m mnoco n m 
oo hi mosmcM coo -^ ono i-voi-oooooo-^m ono N*m^ 


h h h cm co ■*■ mvo soih cm ij-mONCM moo h ■*• o h -*oo m ■* 

HHHHHdtltl CimCOttNflOm 


rt en 

£ 5 

tj u 

H 


cmno h onOnm mONM cmnono r^oo r-. co mvo oo cm ■*■ m cm •<*• 

NONN COONCOI-NONC ro Onno COO r~ m mONCOOHi moo « NO M ID 
NiO n<3 CI m N OiNtO CMOb N -<l-00 ONO CM NOO On M CM ->*-in 


m hi cm CM n -t ifl m N 0> O cm -4-mt^O cot>.o covo O co o O covo 
m m h hi hi cm cm cm m m m Nt Nt Nt UN io m 




Thick- 
ness. 

Inches. 


oooomoncotj- m-^--* ono ono o hi cm -<*-no m m m m •* 
iooo OO hi m + t>oO hi cm co ■>!- moo cm -^-no o c-» r-. t^oo ■*■ 

OOOHIM^MHiMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCMCOCO 


PS 

w 

W 

s 

Q 


Is 1 


■*■ Tt- co -*oo h r--oo r^oo nooo mmrocM oo 

ONO O CM CM Tj-00 H. NO NO NO •*■ CM O 'tNO N CO CO H IT)«OCO CM 

cm co -<*-nc 00 cono O-^-OmomOOOOOOOOCMCM-^-^co 


HHHtittcoro't'f mvo o ooo hi c* co •<*■ mNO t> 


&3 


mto >o mm coiommio 

o * ts -t io » no oo vocMCMCMCMmmm 

■<*- mvo oo cono o cooo m m o unno vovcvo ooo-O O O O O 


MMMHCM«co-<*-T(-m mvo ooo o O « cm ■*■ iovo ooo 


rtlS en 

s is w 


m h h n « mm** «o«0 t^co OiO h ci m* mNO o 









DEN SIT V AND WEIGHT OF WA TEE. 



799 



XXI. 

WEIGHT OF WATER PER CUBIC FOOT FOR VARIOUS TEM- 

PERATURES.* 



Weight of Water per Cubic Foot, from 



to 2i2° F., and Heat- 



units per Pound, Reckoned Above 3? F. 



<u 


■Jt 
X> 






05 

X) O 












JO 




3 


■J.3 


<g 


, 


hJ.5 


m 


, 


— J5 


t/i 


, 


J5 


to 


o.bJa 


, 3 


'5 
3 




2 fc 

Q.V tub 

c b w 

a 3q 




3 


2 fe 

q. J" bit 

r i; U 

§3Q 


iff 


'5 
3 

Q) 


a. « bib 

S 2Q 


Iff 

i) at 


a 
3 

4> 


H 


> 


X 


H~ 


X 


H 


£ 


X 


H 


£ 


X 


32 


62.42 


0. 


78 


62.25 


46.03 


123 


61.68 


91.16 


168 


60.81 


136.44 


33 


62.42 


1. 


79 


62.24 


47-03 


124 


61.67 


92.17 


169 


60.79 


*37-45 


34 


62.42 


2. 


80 


62.23 


48.04 


125 


61.65 


93-17 


170 


60.77 


138.45 


35 


62.42 


3- 


81 


62 22 


49.04 


126 


61.63 


94.17 


171 


60.75 


139.46 


36 


62.42 


4- 


82 


62.21 


50.04 


127 


61.61 


95.18 


172 


60.73 


140.47 


37 


62.42 


5- 


83 


62.20 


51.04 


128 


61.60 


96 18 


J 73 


60.70 


i 4 r. 4 8 


38 


62.42 


6. 


84 


62.19 


52.04 


129 


61.58 


97.19 


174 


60.68 


142.49 


39 


62.42 


7- 


85 


62.18 


53-o5 


130 


61.56 


98.19 


175 


60.66 


I43-50 


-to 


62.42 


8. 


86 


62. 17 


54-os 


131 


61.54 


99.20 


176 


60.64 


14451 


4 r 


62.42 


9- 


87 


62.16 


55-os 


132 


61.52 


100.20 


177 


60.62 


145-52 


42 


62.42 


10. 


88 


62.15 


56.05 


133 


61.51 


IOI. 21 


178 


60.59 


146.52 


43 


62.42 


11. 


89 


62. 14 


57-o5 


134 


61.49 


102.21 


179 


60 57 


x 47.53 


44 


62.42 


12. 


90 


62.13 


58.06 


135 


61.47 


103 . 22 


180 


60.55 


148 54 


45 


62.42 


13. 


91 


62. T2 


59.06 


136 


61.45 


104.22 


181 


60.53 


149-55 


46 


62.42 


14. 


92 


62.II 


60.06 


*37 


61.43 


105.23 


182 


60.50 


150.56 


47 


62.42 


x 5- 


93 


62.IO 


61.06 


138 


61 .41 


106.23 


183 


60.48 


151 57 


48 


62.41 


16. 


94 


62.O9 


62.06 


139 


61.39 


107.24 


184 


60.46 


152.58 


49 


62.41 


*7- 


95 


62.08 


63.07 


140 


6137 


108.25 


185 


60.44 


J53.59 


50 


62.41 


18. 


96 


62.O7 


64-07 


141 


61.36 


109 25 


186 


60.41 


154.60 


5 1 


62.41 


19. 


97 


62.06 


65.07 


142 


61.34 


110.26 


187 


60.39 


155-61 


52 


62.40 


20. 


98 


62 05 


66.07 


143 


61.32 


in. 26 


188 


60.37 


156.62 


53 


62.40 


21.01 


99 


62.O3 


67 08 


144 


61.30 


112.27 


189 


60.34 


157-63 


54 


62.40 


22.01 


loo 


62.02 


68.08 


145 


61 28 


113.28 


190 


60.32 


158.64 


55 


62.39 


23.01 


IOI 


62.OI 


69.08 


146 


61.26 


114.28 


191 


60.29 


159-65 


56 


62.39 


24.01 


1 02 


62.OO 


70.09 


147 


61.24 


H5.29 


192 


60.27 


160.67 


57 


62.39 


25.01 


103 


61.99 


71.09 


148 


61.22 


116.29 


193 


60.25 


161.68 


58 


62.38 


26.01 


104 


61.97 


72.09 


149 


61.20 


117.30 


194 


60.22 


162.69 


59 


62.38 


27.01 


105 


61.96 


73- 10 


150 


61.18 


118. 31 


195 


60.20 


163.70 


JO 


62.37 


28.01 


106 


61.95 


74.10 


151 


61.16 


119. 31 


196 


60.17 


164.71 


61 


62.37 


29.01 


107 


61.93 


75.10 


J 52 


61.14 


120.32 


197 


60.15 


165.72 


62 


62.36 


30.01 


108 


6l.92 


76.10 


153 


61.12 


121.33 


198 


60.12 


166.73 


63 


62.36 


31.01 


109 


61.9I 


77-n 


154 


61.10 


122.33 


199 


60.10 


167.74 


64 


62.35 


32.01 


no 


61.89 


78.11 


155 


61.08 


J 23-34 


200 


60.07 


168.75 


65 


62.34 


33.01 


III 


61.88 


79.11 


156 


61.04 


124.35 


201 


60.05 


169.77 


66 


62.34 


34.02 


112 


61.86 


80.12 


157 


61.06 


125.35 


202 


60 . 02 


170.78 


67 


62-33 


35 02 


"3 


61.85 


81.12 


158 


61.02 


126.36 


203 


60.00 


171.79 


68 


62.33 


36.02 


114 


61.83 


82.13 


*59 


61.00 


127. 37 


204 


59-97 


172 80 


69 


62.32 


37.02 


115 


6l.82 


83 13 


160 


60.98 


128.37 


205 


59-95 


173-81 


70 


62.31 


38.02 


116 


6l.8o 


84.13 


161 


60.96 


129.38 


2d6 


59 -92 


174-83 


7 1 


62.31 


39.02 


117 


6T.78 


85.14 


162 


60.94 


130.39 


207 


59-8g 


175-84 


72 


62.30 


40.02 


118 


61.77 


86.14 


163 


60.92 


131.40 


208 


59-87 


176.85 


73 


62.29 


41.02 


119 


61.75 


87-I5 


164 


60.90 


132.41 


209 


59 84 


177.86 


74 


62.28 


42.03 


120 


61.74 


88.15 


165 


60.87 


J33-4I 


210 


59-82 


178.87 


75 


62.28 


43 °3 


121 


61.72 


89.I5 


166 


60.85 


134.42 


211 


59 79 


179.89 


76 


62.27 


44.03 


122 


61.7O 


90.16 


167 


60.83 


135-43 


212 


59-76 


180.90 


77 


62.26 


45-03 





















Weight of Water at Temperatures Above 212 F. 

Porter (Richards' " Steam-engine Indicator," p. 52) says that nothing- is known about the 
expansion of water above 212 F. Applying formulae derived from experiments made at tem- 
peratures below 212 F., however, the weight and volume above 212 F. may be calculated, 
but in the absence of experimental data we are not certain that the formulae hold good at 
.higher temperatures. 



* Kent's " Pocket-book for Mechanical Engineers. 



8oo 



EXPERIMENTAL ENGINEERING. 



XXII. 

HORSE-POWER PER POUND MEAN PRESSURE. 



O i- 






Speed 


of Piston in Feet per 


Minute. 








G^£ 



100 


240 


300 


350 


400 


450 


500 


550 


600 


650 


750 


4 


.038 


.091 


.114 


.133 


.152 


.171 


.19 


.209 


.228 


.247 


-*8 5 


4* 


.048 


"5 


.144 


.168 


.192 


.216 


.24 




264 


.288 


•312 


.360 


5 


.06 


.144 


.18 


.21 


.24 


• 27 


• 30 




3.3 


•36 


•39 


•45o 


5* 


.072 


•173 


.216 


.252 


.288 


.324 


.36 




396 


.432 


.468 


■540 


6 


.086 


.205 


.256 


.299 


• 342 


.385 


.428 




47i 


•5*3 


•555 


.641 


6* 


.102 


• 245 


• 307 


•39i 


.409 


.464 


.512 




563 


.614 


.698 


.800 


7 


.116 


•279 


.348 


.408 


.466 


• 524 


.583 




641 


.699 


.756 


.874 


7* 


•134 


.321 


.401 


.468 


•534 


.602 


.669 




735 


.802 


.869 


1.002 


8 


• 152 


.365 


.456 


• 532 


.608 


.685 


.761 




837 


.912 


.989 


1. 121 


8£ 


.172 


•4*3 


.516 


.602 


.688 


•774 


.86 




946 


1.032 


1. 118 


1.290 


9 


.192 


.462 


•577 


.674 


.770 


.866 


•963 


1 


059 


i-i54 


1. 251 


1.444 


9* 


.215 


.515 


.644 


• 75i 


.859 


.966 


1.074 


1 


181 


1.288 


1-395 


1. 610 


>o 


.238 


•57 1 


.714 


•83* 


.952 


1. 071 


1. 190 


1 


309 


1.428 


1-547 


1.785 


IOJ 


.262 


.63 


.787 


.919 


1.050 


1. 181 


1-3*3 


1 


444 


1-575 


1.706 


1.969 


II 


.288 


.691 


.864 


1.008 


1. 152 


1.296 


1.44 


1 


584 


1.728 


1.872 


2.160 


Ilj 


■3*4 


•754 


•943 


1.1 


1-257 


1. 414 


1-572 


1 


729 


1.886 


2.043 


2-357 


12 


.342 


.820 


1.025 


1 • i95 


1.366 


I-540 


1.708 


1 


880 


2. 050 


2.222 


2.564 


13 


.402 


.964 


1.206 


1.407 


1.608 


1.809 


2.01 


2 


211 


2.412 


2.613 


3-015 


14 


.466 


1. 119 


^•398 


1. 631 


1.864 


2.097 


2.331 


2 


564 


2.797 


3.029 


3-495 


15 


•535 


1.285 


1.606 


1.873 


2. 131 


2.409 


2.677 


2 


945 


3.212 


3-479 


4.004 


16 


.609 


1. 461 


1.827 


2. 131 


2.436 


2.741 


3-°45 


3 


349 


3-654 


3-958 


4-567 


17 


.685 


1.643 


2.054 


2.396 


2-739 


3.081 


3-424 


3 


766 


4.108 


4 -450 


5-135 


18 


.771 


1.849 


2.312 


2.697 


3-o8 3 


3.468 


3-854 


4 


239 


4.624 


5.009 


5.780 


*9 


•859 


2.061 


2-577 


3 006 


3-436 


3.865 


4-295 


4 


724 


5- I 54 


5-583 


6.442 


20 


.952 


2.292 


2.855 


3-331 


3.807 


4.285 


4-759 


5 


234 


5-731 


6.186 


7.138 


21 


1.049 


2.518 


3.148 


3-672 


4.197 


4.722 


5-247 


5 


771 


6.296 


6.820 


7- 860 


22 


1. 152 


2.764 


3-455 


4.031 


4.607 


5.183 


5-759 


6 


334 


6. 911 


7.486 


8.638 


23 


1.259 


3.021 


3-776 


4.405 


5-035 


5.664 


6.294 


6 


923 


7-552 


8. 181 


9-44 


24 


1-37° 


3.289 


4. in 


4-797 


5-482 


6.167 


6.853 


7 


538 


8.223 


8.908 


10.279 


25 


1.487 


3-569 


4.461 


5.105 


5-948 


6.692 


7-436 


8 


o 7 2 


8 923 


9.566 


11.053 


26 


1.609 


3.861 


4.S26 


5.630 


6-435 


7.239 


8.044 


8 


848 


9.652 


10.456 


12.065 
12.99& 


27 


1-733 


4.159 


s-^o 


6.066 


6.932 


7-799 


8.666 


9 


532 


10. 399 


11.265 


28 


1.865 


4-477 


5-596 


6.529 


7.462 


8-395 


9-328 


10 


261 


n. 193 


12.125 


13.991 


29 


2.002 


4.805 


6.006 


7.007 


8 008 


9.009 


10.01 


11 


on 


12.012 


13.013 


I 5-oi5 


30 


2.142 


5-141 


6.426 


7-497 


8.568 


9.639 


10.71 


11 


781 


12.852 


13923 


16.065 


3 1 


2.288 


5.486 


6.865 


8.001 


9.144 


10.287 


"•43 


12 


573 


13.716 


14.866 


'7-145 


32 


2.436 


5.846 


7.308 


8.526 


9-744 


10.962 


12.18 


13 


398 


14.616 


15-834 


18.270 


33 


2.590 


6.216 


7.770 


9.065 


10.360 


11.655 


12.959 


14 


245 


15-54^ 


16.835 


19.425 


34 


2.746 


6-59 


8.238 


9. 611 


10.984 


I2 -357 


13-73 


15 


103 


16 476 


17.849 


20.595 


35 


2.914 


6 -993 


8.742 


10.199 


11.656 


I3.«3 


14-57 


16 


027 


17.484 


18.941 


21855 


36 


3.084 


7.401 


9.252 


10.794 


12.336 


13.878 


15.42 


.16 


962 


18.504 


20 . 046 


23.130 


37 


3-253 


7.819 


9-774 


11.403 


13-032 


14.861 


16.29 


^7 


919 


I9-548 


21.177 


24 433 


38 


3-436 


8.246 


10.308 


12.026 


r 3-744 


15-462 


17.18 


18 


898 


20.616 


22.334 


25 770 


39 


3.620 


8.648 


10.86 


12.67 


14.48 


16.29 


18. 1 


19 


9i 


21.62 


23-53 


27.150 


40 


3.808 


9-139 


11.424 


13 328 


15.232 


17.136 


19.04 


20 


944 


22.848 


24-752 


28.560 


4i 


4.002 


9.604 


12.006 


14.007 


T6.008 


18.009 


20.00 


22 


on 


24.012 


26.013 


30.015 


42 


4.198 


10.065 


J2-594 


14.693 


16.792 


18.901 


20.99 


23 


089 


25.188 


27.287 


31 485 


43 


4.40 


10.56 


13.20 


15-4 


17.6 


19.8 


22.00 


24 


2 


26.4 


28.6 


33-00 


44 


4.606 


11.046 


13.818 


16. 121 


18.424 


20.727 


23-03 


25 


333 


27 ■ 636 


29-939 


34-545 


45 


4.818 


11.563 


H-454 


16.863 


19.272 


21.681 


24.09 


26 


399 


28.908 


3*-3i7 


36 135 


46 


5.043 


12.086 


15.128 


17.626 


20.144 


22.662 


25-18 


27 


698 


30.216 


32-754 


37770 


47 


5-256 


12.614 


15.768 


18.396 


2 1 . 024 


23.652 


26.28 


28 


908 


^•536 


34.164 


39.420 


48 


5.482 


12.846 


16.446 


19.187 


21.928 


24 . 669 


27.41 


3° 


151 


3a 152 


35633 


41 115 


49 


5-714 


12.913 


17.142 


19.999 


22.856 


25 713 


28.57 


3i 


427 


34.284 


3 ll A1 


42.855 


5° 


5-95Q 


14.28 


17-85 


20.825 


23.8 


26.775 


29-75 


32 


725 


35-7 


38.675 


44-6/25 


51 


6.180 


14.832 


18.54 


21.665 


24.76 


27-855 


30.95 


34 


045 


37.08 


40 . 205 


46.425 


52 


6.432 


!5-437 


19.296 


22.512 


25.728 


28.944 


32.16 


35 


376 


38.592 


41.808 


48 240 


53 


6.684 


16.041 


20 . 052 


23-394 


26.736 


30.078 


33-42 


36 


762 


40.104 


43-446 


50.130 


54 


6.940 


16.656 


20.82 


24.29 


27.76 


31.23 


34-7 


33 


*7 


41.64 


45-" 


5»'0 5 


55 


7.198 


17-275 


21-594 


25-193 


28.792 


32. 39 1 


35-99 


39 


589 


43.188 


46.787 


.S3-985 


56 


7.462 


17.909 


22.386 


26.117 


29 848 


33-579 


3 l 3 l 


41 


041 


44.772 


48.503 


55-965 


57 


7-73 2 


i8.557 


23.196 


27.062 


30.028 


34 794 


38.66 


42 


526 


46.392 


50.258 


57-99 


58 


8.006 


19 214 


24.018 


28, 021 


32.024 


36.027 


40.03 


44 


033 


48.036 


52.039 


60 . 045 


59 


8.284 


19902 


24.852 


28.964 


33-I36 


37.278 


41.42 


45 


562 


48.704 


53.846 


62.13 


60 


8.566 20.558 


25.698 


29.981 


34-264 


38-547 


42.83 


47 


"3 


5I-396 


55-679 


64.245 



WA TER-COMP U TA T/OAT TABLE. 



801 



10 

& • 
3 

z 

w 



w 

H 
cn 

Oh 
O 

w 

< 

B o 

X H 
D 

Oh 

o 
u 

Oh 

w 

H 

«} 
U 

H 
W 

Oh 
O 

w 

H 



» 


O O co OO rJ- tJ- <teo O O O m O co n O O O O *0 Nco 'tO rfco N 
r«» ►* N en t~» ooo coNOOOn^mi-icMiHNeoeo O^o o ^ o Ooo rt 
N N r-» O omONcoNcoinO"<rOOinTi-i-icocoOTt-r^O'-<NNHi 


OO m nmio o m o coo O •** i^ O mo ON ^ n o n ^to o •- en vn 
inco N in O N O O N O OnO O COO O N O ON in O N moo N unco 
m ii n n n ncncn^-'t^-inin invo O O n r> i^>co co co On O O O O O 


00 


in Oco m o t en t Mco OO O in co m co co co OO m cni«r> aNmtn 
O m O co O ino N cow hh rj-r^w rfr co co N in n Tt ■t n tj- O coco O^^O 
\0 O N mifiH loco Oco loi-iO <-> cocoa hoo wm r^cN mt^ OO O O 


O N CO COCO f>NH IflOCONO ^"l^O COO CO M TtO O <■* CO LOCO O '- 
<H/CO i-h inoo N m gvN in O N O O N O ON in O N LOCO N >i->CO >-h in 00 

i-t n n cj n cococo^-Tj-rtLOvnir>000 t>> t>«i^co oo oo OOOO O O 


t» 


moo o i"^ i-* co t^O 'tn OO ^O hh coco-^-^-cor^rj-cN Oco n o -h co 
t^Oi^i-i eoo co-h co in in o coco m'tintoo oco co n s *-• tsooo 
O OO O O t>> »-i ^"Wt H r^cor>>0 O Oco m coco ^•oco^-r^co or* 

co O rt O in O ^-co NO Ocor^O -^r^ON moo O co inco O* n 4o oo 
tj- r^ w unco m loco N in O n in O N loco n loco n inoo n loco m t}-n 
m <-> « n n mntn^^twinifiooo t^r>r^cococo oooo o O 


«s 


O n n i-» O O r» n w hco n t^M n coo co co r)-o inOeor^eooinM 
ON •* O m in O Ocor^O coco ^J- i-t loo lo cn co tj- <n co Oco (T^^O O O 
tninH tj-lon m>h o r>-^fOrtt^ i^o mcooo N r^o n tj-o r^o 


CJ>in«vO mo O ^Ocoo O cor^O coo On Lnr^o n Lnr^On coin 
tnt>.M Ttco « loco m loco n inco n Lnco m Lnco n loco i-i h-nm t r^» 
n i-c n N N cncncnftri-inin uio O O r^ r^ r>.co coco OOOO O O 


13 


oo inco O co O co O tnco unOco o O Oco O O cocoinLnm Lnco co co co 
rt-t-or^O O fNNNoo cor^cio OO r^-r^oo O^D O^O r^O Ln O w 
r^OunoOco n Lnr^O ^00 m tt <t cn n o t--coo^co O N -^r lt> t 


lom r^Nco n r>M Lnocor^o ^-t^O coo O m rfO O >-> ^-o co O n 
cor^O tj- r~~ •— i -3-00 >-< ^t<x> ** inco m loco m t^-co m ^-r^>-c "^-r^O ^r^ 
m m m N N cococo^-^ri-io ununOOO r>. rs i>.oo co oo OOOO O O 


•# 


cn cn'trN O oo cnTtmHcoo in n h Lno O O Oco coOvom m \nOco 
co urtcntNcncn'tH OO Oco vnoo Ooooo OOcoO - H rcocO'5i--+0 co 
O coo rj-Lococo m cocoo r^N t~~0 >-> O OM'h t^-NOco O n con 


Noo Tt-O^Ococo NO O coi^O ^i-r^O N loco m cooco O coint^O 
coo O enr^o ^- r» m rtoo m tj-qo ** 'i-oo m ri-r^M ^fr^o ^r^o coo 

M i-i N N N COCOCOTfra-^LniOLnOOO i>i^r^cococo OOOO O O 


co 


OO^t^t-NOTfNM Ooo O m Or^cooooo lom O n rto co m o r>. 
OLOcooi^r^cOMO'-'OcocOH-LnoOooi-i'-ioo^J'OO^i-'coO'^l" 
'^■r^rj-oo Ooo cor^ooo coOrj-r^co r^o m o co >^ o ^toco O ++ O 


oo >tO lom vnO Ttco NO O eoi^»0 coo ON ir>i^.C covnr^ON ^fO 
no O cor^o ^t^»0 *rNH r^r^i-i r^-r^o ^r^O ^tt^O coo O coo 
»h m cm n N cococOTj-'^-^-LnLn m*0 O O r> t>> r^co coco OOOO O O 


« 


NNrfHiO O '-' O in t-xO CO CO CO in t->CO ^J- <*CO NincOrH OcOLOt^O 

t-t co m ino O ^"co oo m n O r^O coo oO'd-cON t^inr^Noo — O in 
t— ~ •— i Ocoin-^-ON rj-incooino Tj-ir^TfeON (J-\Q t-i r-» m rt inoo oco 


■^■i-O n r^NO n inocoo O »4-r^O coo On tNOw *oco o n 
noo coo O cnt^o cniNO rf/^O rM>0 cor^o coo O coo O coo 
m m i-i n N cOcocOTl-'^-Tj-inin ino O O t>» **» t^»co oooo O^ O^ <J^ O^ O O 


- 


m Tto 0<i Nco N TtO OO cocoOinOoooo O N« NO O Nco JO 
m >h co O in m oo rtO nloOm •-• OO O O'^ ^O O OO cow inOOr> 
O' in cn t^. O O ^too OiOinNr^i-iMNO cy^O co O in O n co in r^O 


m ismoo -1-co cor^NO ocor^O *1" r^ O comoo m cooco w coinr^o 
n inONO Ocoo O coo O cor^-o cn r> O coo O coo Ocoo ON in 
m t-i i-i c< N N cn cn -i- 't t m in ino O O t^» r~* r»co oo co co OOOO O 


tf> 


OOOOOOOOOOOOOOOOOOOOOOOOOOOQO 
Oco mH/H-Tftno -t« r^N ino oo O O O Oco O tmO Onco Oco 
cnoo no into ^i"0 r-^ in m co cn r^ o Oco o cn>-io n i^ o >-" enm^- 


t^.toOinO inO -too mo O cor->0 coo ON inco O cnmNO N ^i-O 
m iT) co NO Ocoo Ocoo O COO O COO OcoO OCOO ONO ON in 
hi M h n n n cn cn cn <t t m m ino o O O t>» f^ r^oo co co OOOO O 




co rf mo r>«oo O O m n cn tj- ino ^«co o O >-> n cn T ino r^oo O O •-• 
^ MWMMMMMWMMMNNNNNNNNNCOeO 



802 



EXPERIMENTAL ENGINEERING. 



C« TO co mwMnmm coco O TtN O co o T N Ocovo nwowihn 
infstM^inoo i-i T r^ O co m T u">co co oco on nc^m co tco r^OO 
w Oco in T N O O h vo O^mMifl O TO co O O Oco O co O *-> N to N 

r^ o O n TO to o>h n mm r^co o •-• n ^ To o r^co o w w co t «^> 
m too m t i^ O co r» o coo o n o on moo w *t r^ o co r^ O coo O 
i_ i_ ,_ c-i n N cnnM^-fti-inifi mo O O r^ t>. r^oo oo co O O O O 



W 
H 

co 

o 

^ s 



T CO MO 't * * 't -t rj- 't Tt O O «oo -tOO N oo T O mml^aH co 

inco O OO O Too wo O OOO -t-UM^oo N r» in in m n r>-o O t>» 

Oco r-» co N mod t O Too co O m o n in r^co Oco r^tnr^oO >-" N m 

cnmNON co TO co CO W W ino co O O m n co T mo f^ O O w n 

■h T t^ O T r^ O coo O cOO ON inco >- inco m T r^ O COO O coo O 

m m m N N N cocococoTTTmin ino O O £>• r>. r^co co co co OOO 



*ClO N inininminuimO T O N O O Tco N O O Too O T N O CO 
inn n cor^N r-»N r^c< r^ co co in o O minNwco r^ r^co O O O O t>» 
r^ r-^ m n O oo coco coo n co coco m to r^co x^o T inco oo <■* O 



d 






<-?* 


_; 


co ^-o r^ 


O O N 


CO i/l\0 


r^co 


O O >-< N 


CO T 


in 


r^-co O 




COO 


o 


COO O N 


in O N 


inco i-i 


T r^ O T r^ O 


COO 


O n inco 


£ 




M CS 


N 


N 


cOcococOTTTin 


in inO O O 


t^ t^ r^co co co 


oo 


OOO 



C-i Ocoo T T T T T T TO co O N TO oo O n TO oo conh in o co 
in i-i TO co T O O N co TO i^mo con coi-^n Oco O^^O co in in ooo 
inincoOco tMDH t-»i-i inOO NO O co inO r~^0 in co TO co O O O 

r» o i-i co TO co O m co TO r^ O O n co T ino r^co o O w n co t u"> 
O coi^O coo Ocoi^ON inoo m inco w T r->. O coo Ocoo ON inoo 
m m m m « N n cococoTTTinininooO M^t^t^oocooo OOO 



OOOOcococococococoOOOOOOOOOOOOcocococococo 
in n r^ O O^^O coOr^T'-'ONONOONONOONcoocoT Ooo 
co ^ m o^^ incoo i^>C Tj-OinO inON ^ ino O io co co in r^co oo oo 

rfOcoO'-"coinr^coOi-iN^tor^ooOt-<NcoTj-inor^>cooOi-iN 
O coo O coo O N in o N inco i-i ^ r-- w -xj- t^ O coo O N inco n inco 
M M m m cm N N cococo-i-'vi-'^-inin ino O O r^. r^ r-^ r^oo co oo O O O 



X 
X 



< 

!Z! ^ 

c 
u 

tk 

H 

H 

< 

< 

u 

c-i 

w 
c^ 


uJ 
H 



OcoONOOOOOOO'^-NOcoO'^-NOcoO'^-N>-ir-~cooi^ k -' 
rtN ocoOcoo 'i-N Oco coo i-i r^o r^o m m o i-i ^ >-i ■«■ n coOO 
m m OMncnnto ^ON r^coOcor^O co^-nin^t-N N rfO r^r^-r^ 

m cotOco O N coinoco 0"-< N ^-in l^co O O *- N co rf inO r^co O 
O coo ONO On inco i-i ^too m ^ r-^ O coo O coo On inco w •+ r^ 
t-i hh hi i-i cm n N cococoTj-'^-Tj-inin ino O O r>. r-» r>. r^oo co oo o o O 



N O O ^f t^. J^ NNNtN »>>o NCO ^00 Nco ^Oi^-N n-o CO O N rf 
Tt co -I o O Oco i^>0 in ^O O in co co 'l-co com >i noco n O coOO 
O Oco in co hh O^kO n r^M m n r^NO Ow cO'^-^teoi-' O co ino O O 



r^ 


O M 


co in r^co 


d 


N co ino co 


o 


^ 


N co inO 


r^co 


OO w 


N CO 


■n- 


ino 


ONO 


O N 


in oo 


N 


inco m 'd- r^ o 


rh r- 


O N 


in O N 


inco 




-+■ i^ 


o 


1-1 ^ 


M N 


N N 


CO CO CO Tf ^J- *J" 


in 


in 


ino O o O r^ r-~ r^co co co 


O^ O^ O^ 



ci'tcq om 



^O coONrfinr^OONco ino co O O N co rf tnO r^ r^ O O "-i N co 
On in o n inco w rtoo m ^ r>. O coo O coo On inco w -too i-i -T r^ 
O m m i- n n n cococOTt'<Trtinin ioo O O O r-» r^ r^co co co o O O 



coo tn r^r^r^r>.r^r^t^O n to co o n TO coon ocor^Mino 
N TTN m NCOT inO r>i coco inTi^OTn O m inO Nco r> i-i co O 
in in T N Oco O co O Too N co T O COO OmnnmOcoONTTT 

i-i co in r^co o n T in r~»co o •-< to TO r^co O m n co t TO r^oo o O 
On inco i-i inco >-< TX-^O Tt~-»0 coO ONO ON inco m Tr^O cor~« 
O m m m n n n cococoTTTininininooo r>r>r^oococo a^ 0~- O^ 



000000000000000000000000 
TO co O N TO NOONONOONONOOOOCOO 
O Ti-ico cot^O t^ coco n inco O m i-i O o r^ O >h cocoT 



00000000 
N ino in N 
co co N O r-^O 

co O N T »n r>» O m N T»^ l">-co O t-i co T in r^co O O O w N T 
co n inco i- Tr^i-iTr^OcooOc-io ONincOMinooi-i Tr^ 
q m i-h hh N N N cococoTTTinir, in ino O O r^ f^ r^oo co oo 



COEFFICIENT OF DISCHARGE. 



803 



The following tables give coefficient of discharge as collated 
from Hamilton Smith's experiments by Professor Merriman. 

XXIV. 

WEIRS WITH PERFECT END CONTRACTION. 









Length of Wei 


r in Feet. 






Effective 














Head 
















in Feet. 


0.66 


1 


2 


3 


5 


10 


19 


O.I 


0.632 


0.639 


0.646 


0.652 


0.653 


0-655 


0.656 


0.15 


.6:9 


.625 


• 634 


.638 


.640 


.641 


.642 


0.2 


.611 


.618 


.626 


.630 


.631 , 


•633 


•634 


0.25 


.605 


.612 


.621 


.624 


.626 


.628 


.629 


°-3 


.601 


.608 


.616 


.619 


.621 


.624 


.625 


0.4 


• 595 


.601 


.609 


.613 


.615 


.618 


.620 


0.5 


.590 


• 596 


.605 


.608 


.611 


.615 


.617 


0.6 


.587 


•593 


.601 


.605 


.608 


.613 


.615 


0.7 




•59o 


.598 


.603 


.606 


.612 


.614 


0.8 






•595 


.600 


.604 


.611 


.613 


0.9 






•592 


• 598 


.603 


.609 


.612 


1.0 






•59o 


• 595 


.601 


.608 


.611 


1.2 






.585 


• 591 


•597 


.605 


.610 


1.4 






.580 


•587 


•594 


.602 


.609 


1.6 








.582 


•59i 


.600 


.607 



* See p. 274. 

XXV. 
WEIRS WITHOUT END CONTRACTION. 









Length of Weir in Feet. 






Effective 














Head 
















in Feet. 


2 


3 


4 


5 


7 


10 


19 


O.I 








0.659 


0.658 


0.658 


0.657 


0.15 


0.652 


0.649 


0.647 


•645 


•645 


.644 


• 643 


0.2 


• 645 


.642 


.641 


.638 


• 637 


•637 


.635 


0.25 


.641 


.638 


.636 


•634 


•633 


• 632 


.630 


3 


• 639 


.636 


.633 


.631 


.629 


.628 


.626 


0.4 


.636 


•633 


.630 


.628 


.625 


.623 


.621 


0.5 


•637 


• 633 


.630 


.627 


;624 


.621 


.619 


0.6 


.638 


•634 


.630 


.627 


•623 


.620 


.618 


0.7 


.640 


.635 


.631 


.628 


624 


.620 


.618 


0.8 


.643 


• 637 


•633 


.629 


•625 


.621 


.618 


0.9 


.645 


•639 


•635 


.631 


.627 


.622 


.619 


1.0 


.648 


.641 


•637 


.633 


.628 


.624 


.619 


1.2 




.646 


.641 


.636 


.638 


.626 


.620 


1.4 






.644 


.640 


•634 


.629 


.622 


1.6 






• 647 


.642 


.637 


.631 


.623 



8o4 



EXPERIMENTAL ENGINEERING. 



XXVI. 

HORSE-POWER LINE-SHAFTING WILL TRANSMIT WITH SAFETY 

Bearings, 8 to io ft. centres. 



Diameter of 


Horse-power 


Diameter of 


Horse-power 


Diameter of 


Horse-power 


Shaft 


in one 


Shaft 


in one 


Shaft 


in one 


in Inches. 


Revolution. 


in Inches. 


Revolution. 


in Inches. 


Revolution. 


15 
TF 


.008 


2Tf 


.216 


Sit 


.728 


ifV 


.0156 


3-h 


.272 


61V 


2.195 




.027 


3tV 


•343 


6H 


2.744 


.043 


3H 


.424 


7* 


3.368 


i T f 


.064 


3tI 


.512 


711 


4.O96 


2A 


.091 


4 ?f 


.728 


8t 7 6 


4.912 


2 T V 


.125 


4if 


I. OO 


8if 


5.824 


2H 


.166 


5tV 


I.328 


9A 


6.848 



For jack-shafts, or main section of line-shafts, allow only three-fourths of 
the horse-power given above, and also provide extra bearings wherever heavy- 
strains occur, as in main belts or gears. 



XXVII. 

HORSE-POWER BELTING WILL TRANSMIT WITH SAFETY. 



Hors 


e-power per ioo Feet. 




Horse-power 


per 100 Feet. 


Width of 


Velocity of Belt. 


Width of 


Velocity 


of Belt. 


Belt 




Belt 
in Inches. 






in Inches. 










Sing! 


e Belt. 


Double Belt. 




Single Belt. 


Double Belt. 


I 


09 


.18 


12 


I.09 


2.18 


2 


18 


.36 


14 


I.27 


2-55 


3 


27 


•55 


16 


1-45 


2.91 


4 


36 


•73 


18 


I.64 


3.27 


5 


45 


.91 


20 


1.82 


3-64 


6 


55 


1.09 


22 


2.00 


4.00 


7 


64 


1.27 


24 


2.18 


4-30 


8 


73 


1.46 


28 


2-55 


5 09 


9 


82 


1.64 


32 


2.91 


5.82 


10 


9 1 


1.82 


36 


3-27 


6.55 


11 1 


00 


2.00 


40 


3.64 


7.27 



In the calculations for horse-power in the above table, the belt is assumed 
to run about horizontally; the semi-circumference of smaller pulley has been 
considered as the ordinary arc-contact of belt. Any reduction of this contact 
will make approximate proportional reduction of horse-power. 



DEFT. EXPERIMENTAL ENGINEFRINC, BIBL'EY COLLEGE, CORNELL UNIVERSITY. 
































































































































































































































































































































































































































































































































































































































































































4-i ~ r 
















































































































































































































































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T X i i 














































































































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A. C. CARPENTER. ITHACA N. 



ANDRUS & CHURCH, Publ.shem. 
ITHACA, N- Y. 



INDEX. 



A 

PAGE 

Abrasion Test 186 

" " Paving-brick 180 

Absolute Pressure 336 

" Zero........ 338 

Absorber in Refrigeration 747 

Absorption Dynamometer 235 

Test of Bricks 179 

Accelerated Cement Test. v 190 

Accidental Errors 18 

Accuracy of Numerical Calculations 19 

Acidity Tests for Oil 215 

Adiabatic Compression, Loss of Work by 729 

' ' Curve fer Gases 712 

' ' for Steam, Formula for 556 

' ' Curves for Ammonia 745 

1 ' Definition 342 

' ' Expansion of Gases 711 

w " Steam, Formula 554 

Admiralty Tests 172 

Admission -line Diagrams. . . 564 

Air, Coefficients of Discharge 298 

" Formulae for Adiabatic and Isothemal expansion 711 

" " Flow of in Pipes 711 

1 ' Measurement of Velocity. 306 

" Velocity of Flow 297 

1 ' of, Measured by Heating 726 

" Volume Discharged. . . .' 296 

" Weight " 298 

807 



80S INDEX. 



Air-compressor, Clearance Space 723 

' ' Data and Results, Tests of 730 

" Formulae for Compression 711 

" Types of — 720 

Air -pyrometer 381 

Air Refrigerating-machine 741 

Air-thermometer 371 

' ' Construction. : ; 376 

' < Corrections ' 377 

1 i Directions for 378 

' ' Form of 379 

' ' Formula for 374 

' l Uses of 377 

Alcohol Thermometer 371 

Alden Brake • 241 

Allen's Draft-gauge 351 

Ammonia Absorption System 748 

Illustrated 750 

' ' Adiabatic Curves for 745 

' ' Anhydrous Properties of. . 740 

' ' Compression Cylinder 744 

" u Relation of Pressure and Volume 711, 744 

Gauge. . . 358 

1 ' Refrigerating-machine 742 

' l Refrigeration Data and Result Sheets 749 

Amsler's Planimeter 30 

Analysis of Flue -gas 474 

' < Proximate, Coal and Coke 470 

Analyzer in Refrigeration 747 

Anemometer Calibration 307 

' ' Described 306 

' ' for Measuring Air 725 

Angles, Functions of, Table 771 

' ' Table of Natural Functions 777 

Anhydrous Ammonia, Properties of 738 

Approximate Calculation, Formulas 16 

Artificial Building Stone, Test of. 178 

Ash Analysis, Table 787 

Ash, Determination of 47° 

Ashcroft's Oil-testing Machine 227 

Asphalt, Tests of 180 

Aspirator for Flue-gas 478 



INDEX. 809 



PAGE 



Atmospheric Line 548 

' ' Pressure 336 

Atomic Weight Definition 443 

Autographic Apparatus, Olsen m 

" Diagrams 21 

' ' Extensometer 133 

Torsion Machine 114 



B 

Bachelder Dynamometer 255 

' l Indicator 523 

Back -pressure Line 549 

Barnett Gas-engine 702 

Barrel Calorimeter 402 

* ' " Directions 405 

Barrus Continuous Calorimeter 410 

' ' Superheating Calorimeter 398, 416 

Bauschinger's Extensometer 125 

Beau de Rochas Cycle 702 

Beaume's Hydrometer Scale, Table of 786 

Belt Test, Directions 266 

" " Forms 268 

' ' Testing Machine 264 

' ' Dynamometer 263 

' ' Friction '. 199 

" Testing Methods 263 

Belting, Table of H.P. 304 

Bending Moment 76 

Test 166 

Bernoulli's Formula 276 

Berthelot's Fuel-calorimeter 457 

Berthier's Fuel-calorimeter 456 

Blowers, Types of 723 

Boiler Efficiency 493 

' ' Horse-power 494 

' ' Leakage Locomotive Test 648 

1 ' Test, Abbreviated Directions 514 

Form •• 5i3 

" " Analysis of Coal 504 

1 1 " Analysis of Flue-gas 504 

" " Calculations of Efficiency 505 



8io 



INDEX. 



Boiler Test, Calibration of Apparatus 497 

" * ' Correction for Leakage 498 

' ' " Definitions 493 

' ' ' ' Duration 499 

11 " for Locomotives 639 

' ' * ' Forms for Data and Results 507 

" Fuel 49 6 

" " Value 472 

' ' " Graphical Log . . 495 

" " Heat Balance 506 

' ' ' ' Measurements 496 

" Object 492 

" ' - Pumping-engines 618 

" " Quality of Steam 501 

11 Records 501 

" " Sampling of Coal 502 

* ' ' ' Smoke Observations 506 

" " Standard Method 495 

" ( * Starting and Stopping 499 

" ' ( Uniformity of Operations 500 

Boiling-point, Table 423 

Test for 380 

1 ' Test for Cement 190 

Bomb Fuel-calorimeter 457 

Boston Extensometer 132 

Boult's Oil-testing Machine 227 

' ' " ' ' Directions 230 

Bourdon Gauge 357 

Boyer Speed-recorder 650 

Brake, Alden 241 

' ' Constants 244 

■ ' Designing. 236 

1 ' Different Forms 239 

' ' Directions for Use 243 

1 ' Fan Form 245 

1 ' Horse-power 239 

' ' Hydraulic 242 

" Prony 235 

' ' Pump Form 245 

' ' Self -regulating 241 

' ' Strap Stresses 235 

4 ' Transfer of Heat 243 



INDEX. 



8ll 



Breast Water-wheels 313 

Brick, Abrasion Test 180 

" Test of 178 

Bridge Material, Specifications 169 

Tests '. 168 

Brine, Specific Heat of 752 

Briquettes, Form of 141 

Brown Speed-indicator 573 

Brumbo Pulley 531 

Burning-point Test for Oils 212 

Buzby Extensometer I2 7 



Calibration of Anemometer 307 

1 ' Apparatus for Engine Test 578 

' ' Differential Dynamometer 256 

' ' Drum Spring 542 

Forms for Gauges 368 

of Gauges 363 

' ' Gauges with Mercury Column 366 

1 ' Indicator Spring 535 

' ' Morin Dynamometer 249 

1 ' Planimeter 52 

' ' Tachometer 291 

' ' Testing-machins 97 

" Venturi Tube 287 

" Weir 285 

Caliper, Micrometer 59 

" Sweet 60 

' ' Vernier 57 

Calorie 339 

Calorific Power of Fuels 444 

Calorimeter, Barrel 402 

Barrus Continuous 410 

' ' Superheating 416 

Chemical 440 

Collecting- nipples 399 

Comparative Value 441 

Condensing 395 

Continuous-jet Condensing 405 

Diagram for Results from Temperatures 428 



812 



INDEX. 



Calorimeter, Diagram for Throttling 425 

' c Effect of Errors ,....' 396 

Forms 4I4 

Fuel, Bomb 457 

" " Heat Equivalent 452 

" Mahler's 4 6i 

11 " Thompson 455 

' ' Hoadley 407 

Injector 4 o6 

1 ' Limits of Throttling 427 

1 ' for Locomotive Tests 653 

Measure of Water Equivalent 4 oi 

Method of Sampling Steam 399 

Principles of Fuel 45! 

Separating 430 

Formula for Use 436 

Superheating 398 

Table of Errors 397 

Throttling 4I 8 

Diagram for using '. 796 

" " Formula. 398 

" Table for using 795 

Use of, on Pumping-engine 621 

Calorimetric Method of Engine Testing 590 

' ' Pyrometer 381 

Capacity of Pumps, Definition 329 

How Computed 628 

Carbon, Determination of 470 

' ' Dioxide Absorbents 475 

' ' Monoxide Absorbents 476 

Carbonic Acid Absorbents 475 

Carburetter 709 

Car-wheel Tests 167 

Carnot Cycle for Gas-engines 714 

Carpenter Calorimeter for Steam 422 

' ' Draft-gauge 35 1 

' ' Fuel-calorimeter 463 

' ' Separating-calorimeter 435 

Cast-iron Tensile-test Piece 139 

Cathetometer 62 

Cement, Definitions 181 

1 ' Fineness Test 184 






INDEX. 813 

PAGE 

Cement Moulds i 4I 

' ' Natural, Definition T g T 

* ' Normal Consistency Test 185 

" Portland, Definition i 9I 

I c Sieves 184 

II Specific Gravity Test 183 

1 ' Specifications 190 

' ' Tensile Strength Required 192 

" Test, Mixing 187 

" Piece 140 

' ' Tests, Forms for 194 

Testing 182 

Tensile 189 

1 ' Machine 119 

Fairbanks 120 

Olsen 121 

Riehle 122 

Centrifugal Blower, Data and Results 732 

Theory of 729 

Fans, Types of 724 

Pumps, Test of 331 

Chain-test Piece 139 

Chemical Calorimeter 44 

' ' Equivalents, Table 444 

Chill-point Test of Oil 214 

Chloride of Calcium, Specific Heat 752 

Chromous Chloride 475 

Chronograph 573 

" Record 576 

Chronometer for Locomotive Testing 650 

Cistern Manometer 347 

Classification of Calorimeters 391 

Clay-ball Pyrometer 389 

Clearance, how measured 583 

from Indicator Diagram 560 

in Compressor, Effect of 728 

' ' Line 548 

Coal and Coke, Proximate Analysis 470 

" Calorific Tests 504 

' ' Method of Determining Moisture 502 

' ' Sampling 502 

1 ' Test, Form of Report for Locomotives 644 



8 14 INDEX. 



PAGE 



Coal Test on Locomotives 642 

Coefficient of Discharge 271 

' ' " Friction .' I9 6 

Coffin Planimeter 4I 

Cold Tests for Oil 213 

Column Testing, Directions x ^ 4 

Combined Diagram, Method of Drawing 566 

' ' Inertia and Indicator Diagrams 668 

Combustible, Definition 403 

Combustion, Definition 44 ^ 

Heat of, Table 44 6 

Method of Determining when Perfect 452 

' ' Products, Object of Analysis . .' 4 73 

' ' Temperature, How Determined 448 

Composition of Fuels, Table 4 ^ x 

Compound Engine Diagrams 565 

' ' " Hirn's Analysis 604 

' ' Pumping-engine Test Examples 631 

Compressible Fluids, Flow of 295 

Compression, Effect of Clearance 728 

' ' Formula 74 

' ' of Gases, Formula for y TI 

Test, Directions 154 

1 ' Pieces 142 

" Results I55 

Compressor, Ammonia 742 

" for Air, Test of 730 

' ' Types of 720 

Computation Machine 64 

Condensation in Cylinder 561 

Condenser for Steam, Surface 576 

Test 578 

Condensing Calorimeters 395 

Consistency, Normal, Test of 185 

Constancy of Volume, Definition 189 

" " Test I02 

Constant Head Viscosometer 207 

Contraction, Coefficient for 271 

Cornell University Experimental Engine. 657 

Corradi Roller Planimeter 45 

Counter of Speed 572 

Crosby Gauge-testing Apparatus 363 






INDEX. 8 1 5 

PAGE 

Crosby Indicator 521 

Cross-section Paper 20 

Curtis Steam-turbine 690 

Curve, Adiabatic, Formula for Steam 556 

- ' Isothermal, Formula for 557 

' ' of Expansion Steam 556 

" " Saturation, Formula for 555 

Cycle, Four-stroke 702 

' ' Two-stroke 702 

' ' of Gas-engine 713 

' ' " Refrigerating Machine 734 

Cylinder Condensation 561 

Loss by Diagram. 563 



t i 



D 

Definitions, Friction Tests 196 

Steam-engine Terms 569 

Deflectometer 135 

Degree of Superheat 390 

" " " Formula for 393 

DeLaval Steam-turbine, Description of 687 

Density of Steam 342 

' ' Test, Oil 202 

Diagram, Autographic 21 

1 ' of Experiments 20 

1 ' from Indicator, Combined 567 

" " Indicators 563 

1 ' Inertia '. 664 

1 ' Locomotive Tests , . 652 

1 ' Reduction of 22 

Represents Work 21 

" of Shaft Motion 567 

11 Strain 69, 144 

for Throttling-calorimeter . 405 

Thurston's Torsion Machine 115 

Diameters and Squares, Table of . ... . 756 

Diaphragm, Discharge through . . . . . 280 

Gau g e 359 

Loss of Head through 279 

Diesel Oil-engine . > JO g 

Differential Dynamometer 255 

" " Calibration 256 



8i6 



INDEX. 



PAGE 

Dilution Coefficient 488 

Dimensions, Experimental Engine, Institute of Technology 605 

Sibley College 657 

of Pipe, Table of 798 

Directions for Belt Test 266 

" Tension Tests 145 

Discharge, Coefficient for 271 

Draft Gauges 351 

Draw-bar Pull of Locomotives 649 

Drop Test, Directions 164 

' ' Testing Machine 119 

Drum Motion of Indicator 540 

' ' Spring Calibration 542 

" ' ' Testing Device 541 

Ductility of Specimens 143 

DuLong's Formula 445 

Durability Test Lubricants 226 

Duty, Definition 328 

' ' How Computed 628 

' ' Test, Pressure-gauge 620 

1 ' Trial, Pumping-engines 618 

Dynamometer, Absorption 235 

1 ' Alden 241 

Belt 263 

' ' Classes of 235 

' ' Differential 255 

* ' Emerson's 259 

1 ' Horse-power 517 

1 '■ Lewis 252 

" Locomotive Tests 651 

" Pillow Block 252 

1 ' Records, Locomotive Tests 649 

" Steelyard 250 

" Traction 246 

** Transmission 247 

" Van Winkle : 261 

" Webber 255 

E 

Efficiency, Boiler 494, 5°5 

1 ' of Ideal Refrigerating Machine 735 

1 ' Mechanical, Definition 569 



INDEX. 



8l 7 



Efficiency of Perfect Engine 570 

" Plant ! 570 

' ' " Refrigerating Machine 736 

1 ' Test of Pumps 330 

1 ' " Steam-engines 589 

" .- -.-. 3 

Thermodynamic, Definition 570 

Elastic Curve 159 

Elasticity 68 

' ' Modulus 73 

1 ' and Rigidity Modulus, Relation of 8^ 

Elbows, Loss of Head 277 

Electric Ignition 704 

' ' Pyrometer 385 

Elliott's Flue-gas Apparatus 479 

Elongation, in Test Piece . . 68 

Measure of 134 

Emerson's Power Scale 259 

Emery Scale Beam 106 

' ' Testing Machine 94, 96 

1 ' Vertical Machine 102 

1 ' Weighing System 106 

Empirical Formula, How Deduced 10 

Engine Fitting for Testing 582 

1 ' Hot-air 694 

1 ' Inertia of Parts 660 

' ' Locomotive Test. 652 

1 ' Method of Measuring 583 

" Methods of Testing 581 

1 ' Water Pressure 309 

1 ' Test, Calibration of Apparatus 578 

Directions 585 

Form for Results 584 

Indicator Practice 584 

for Leaks 582 

Measurement of Speed 571 

Object 570 

Quality of Steam 581 

Weighing Steam 581 

Entropy, Definition '. 343 

' ' Table of 794 

Ericsson Hot-air Engine 694 



8 1 8 INDEX. 

PAGE 

Ericsson Hot-air Engine, Method of Operating 700 

Errors, Classification of ' 5 

1 ' Combination of 9 

" Probability of 6 

' ' When to Neglect '. 18 

Euler's Formula , . 75 

Evaporation, Table of Factors 797 

Expansion Curve, Method of Drawing 554 

■ ' Fuel Calorimeter 463 

' ' of Gases, Formula for 711 

1 ' Ratio of = 550 

Experiment vs. Theory 2 

Experimental Engine Dimensions, Institute of Technology 605 

" " Sibley College, Dimensions of 657 

" Use of 656 

Experiments, Classification 3 

Objects of 1 

Extensometer, Autographic 133 

' ' Bauschinger's 125 

1 ' t Boston 132 

" Buzby 127 

" Henning 129 

" How to Apply 148 

" Johnson's 129 

" Marshall 131 

" Paine 127 

" Riehle 128 

" Roller and Mirror 125 

" Strohmeyer's 126 

" Thurston 129 

a ' Unwin's 126 

" Wedge 124 

Eye-bars, Specifications of 171 

F 

Factor of Safety 69 

' * ' ' Evaporation, Definition 493 

Factors of " Table ■ 797 

Fairbanks Cement Machine 120 

' ' Testing Machine 92 

Fan Brake 245 

Fan, Data and Results 732 






INDEX. 819 



PAGE 



Fan, Theory of 729 

Fans, Types of 724 

Fatigue of Metals 166 

Favre & Silbermann Fuel Calorimeter 453 

f eed-water Measurement 616 

" Temperature, Determinations of 615 

Fineness of Cement 192 

Test 184 

Flash Test of Oils 210 

Floats 282 

1 ' Use of 289 

Flow of Air 296 

" "in Pipes 299 

1 ' Compressible Fluids ■ 295 

1 ' Gas 302 

' ' Steam through Orifice 300 

I * Water in Pipes 288 

" " Measurement of 281 

Flue-gas Analysis, Computations from 486 

Forms and Computations 490 

Methods 474 

Object of 473 

" " Process of 476 

11 " Reagents 475 

{ ' Aspirator 478 

1 ' Sampling of . 477 

Flue-gases, Analysis of . . 504 

Flue Losses from Flue-gas Analysis 488 

Fluid Friction 200 

P orging Test 166 

Form for Data and Results Steam Injector. . 681 

* * Record, Locomotive Tests 646 

* * Report of Test, Steam-turbine 693 

* ' " Report, Pumping Test 624 

II Results of Engine Test 584 

• ' Tension Test. 151 

" Test of Pulsometer 684 

Forms for Air Thermometer 379 

* ' •"' Belt Test 268 

11 rt Calibration of Gauges 368 

' ' • 4 Calorimeter 414 

" " Cement Test 194 



820 



INDEX. 



Forms for Hirn's Analysis 598 

" " Oil Test 233 

" " Pump Tests 332 

" " Separating Calorimeters 439 

11 " Test, Hot-air Engine 698 

" " Testing Hydraulic Motors 326 

1 ■' " Throttling-calorimeter 430 

Formula, Air Thermometer 374 

1 ' Bernouilli 276 

' ' for Approximate Calculation 15 

" Compression 74 

' ' Empirical, Deduction of 10 

" " Friction 198 

" " Pressure, Volume and Temperature, Relations of Gases. . . 711 

Formulae for Hirn's Analysis 591 

Freezing Machine, Cycle 734 

Point of oil, Test for 380 

Friction, Classification 197 

' ' Coefficient of 196 

' ' Formula . 197 

1 ' Lubricated Surfaces 201 

of Belts 199 

" Fluids 200 

" Gears 199 

" " Journals 198 

" " Pivots 198 

Table of Coefficients 784 

Test of Engine 589 

1 ' Tests, Definitions 196 

Frost Test for Stones 176 

Fuel Calorimeter, Bomb 457 

Calorimeters, Principle of 451 

Consumption, Definition 569 

Measurements, Locomotive Testing 641 

Method of Sampling 452 

Test, Locomotive 635 

Value by Boiler Trial 472 

Weight of, Engine -testing 582 

Fuels, Composition of 451 

' ' Table of Composition 787 

Fulcrums for Emery Machine 95 

Fuller's Slide Rule 28 



INDEX, 



821 



Furnace Efficiency from Flue-gas Analysis 489 

' ' Maximum Temperature from Flue -gas Analysis 488 



Gas Analysis Apparatus 479 

1 ' Composition of, Table '703 

' ' Measurement of Flow 302 

Gas-engine, Classification 700 

Compression Type 702 

Cycles 713 

Diagram 716 

Four-cycle 706 

Ignition 703 

Indicator 524 

Optical Indicator 525 

' ' Report of Test 716 

Theory 711 

Two-cycle 707 

Gas Measurement, Dry Meter 305 

" " Wet Meter 303 

' ' Meter, Testing Device 303 

Gasoline Engines 708 

Gas- or Oil-engine Testing 714 

Gauge, Apparatus for Testing 363 

" Calibration by Mercury Column 366 

' ' Correction of. 367 

' ' Makers, list of 36 1 

1 ' Marking Device 113 

' ' Tension Test 147 

Gauges, Recording 613 

■ ' for Steam-pressures 357 

Gear-teeth Friction 199 

Gibbs's Viscosometer 205 

Giffard Injector 670 

Graphical Log of Boiler Test 495 

' ' Multiplication 64 

' ' Representation of Data 20 

Gumming or Drying Test 210 



H 

Hammer Test 166 

Hancock Inspirator 672 



822 



INDEX. 



PAGE 

Hardening Test 166 

Head, Lost by Contraction 279 

11 " at Elbows 279 

* ' ' * " Entrance of Pipe 278 

1 ' " in Perforated Diaphragm 279 

1 ' ' ' " Pipes, Measurement of 289 

" "by Valves , . 279 

1 ' Producing Velocity 271 

1 ' Relation to Pressure 324 

1 ' of Water, Measurement of 281 

Heat Application to Isothermal Expansion 713 

1 ' Balance 494 

" " in Boiler-testing 506 

1 ' of Combustion 444 

1 ' Consumption, Ideal Engine . . 569 

1 ' Equivalent of Fuel Calorimeter 452 

* ' Interchanges from Saturation Curve 612 

* ' Losses in Refrigerating Machine 738 

" Mechanical Equivalent of 339 

" Specific, definition 338 

" "of Brine 752 

1 1 and Temperature 337 

" Transfers of Refrigerating Machine 735 

i { Units, definition 339 

' ' " per Horse-power 569 

Heating Value Measured by Oxygen 446 

Heisler Calorimeter 421 

Hempel's Flue-gas Apparatus 483 

' ' Fuel Calorimeter 456 

Henning Extensometer 129 

Hennings's Mirror Extensometer 130 

Higgins's Draft-gauge 353 

Hirn's Analysis 590 

11 " for Compound Engine 603 

" " Directions for 595 

" " Forms for 598 

tc " Institute of Technology Engine 605 

" " for Non-condensing Engine 603 

11 il by Saturation Curve 611 

" ' ' for Triple -expansion Engine 604 

Hoadley Air-thermometer 372 

' ' Calorimeter 407 



INDEX. 823 



Hoadley's Calorimetric Pyrometer 384 

Draft Gauge 353 

Hook Gauge 282 

Hornsby-Akroyd Oil-engine 711 

Horse-power, Boiler 494 

" Brake 239 

1 ' Formula for 517 

Method of Computing 552 

" per Pound M.E.P., Table . . . 800 

Hot-air Engines 694 

1 ' Engine Forms 698 

" Theory 697 

Hot Test for Cement 192 

' ' Tube Ignition 704 

Humidity of the Air, Table 785 

Hydraulic Engines 309 

' c Machinery, Classification 308 

' ' Motor, Forms for Testing 326 

' ' Power System, Parts of ' 309 

' ' Ram 321 

11 " Directions for Testing 325 

' ' Testing Machine 92 

Hydraulics, Flow of Water 270 

Hydrometric Pendulum 295 

Hyperbola, Method of Drawing 554 

Hyperbolic Logarithms, Table of 784 



Ice-making Plant, Illustrated 746 

Ignition, Methods of, in Gas-engines 703 

Impact Test, Directions 163 

' ' Testing Machine 119 

Impulse Steam-turbine, Description of 687 

' ' Water-wheel 314 

Indicated and Dynamometric Power 516 

' ' Horse-power 517 

" " Method of Computing 552 

Indicator, Applied to Locomotive 636 

" Attachment to Cylinder 543 

' ' Attachments, Engine -testing 582 

Care of ( 545 



824 INDEX. 



PAGE 



Indicator Cock 543 

1 ' Cord 529 

11 " Attachment of .■ 532 

" ' * Tension on 541 

" Diagram 516 

* ' " Clearance, How to Find 561 

" " Combined 567 

" " Definitions 547 

" " General Discussion 562 

' ' " Form for Ideal Case 553 

" " Hot-air Engine 699 

" " with Loop 552 

' ' * ' Weight of Steam from 557 

1 ' Diagrams, Measurements of 551 

" ' ' Method of Taking 544 

' ' Dimensions, Table of 528 

1 ' Drum Motion 540 

1 ' Early Forms 517 

1 ' External Spring 523 

1 ' for Gas-engines 524 

Gas-engine, Use of 715 

1 ' Gear for Locomotives. 638 

' ' for Inertia 661 

Optical 525 

' ' Paper Drum.. 529 

Parts • 526 

1 ' Pencil Mechanism 526 

" " Movement Test 539 

1 1 Practice, Engine Test 584 

' ' Reducing Motions 529 

Spring 527 

" Calibration 535, 579 

' ' Standardization 534 

1 1 of Steam-engine, Use of 515 

' ' Tests of Locomotive, Form for. 653 

Inertia Diagram 664 

' ' Indicator 661 

1 1 and Indicator Diagram Combined 668 

' ' Moment, Experiment for 80 

' ' Moments, Table 78 

' ' of Parts of Steam-engine 660 

Injector, Directions for Testing 679 



INDEX. 825 



PAGE 



Injector, General Directions for Use 679 

1 ' Limits of 676 

' ' Mechanical Theory 674 

' ' Thermodynamical Theory 672 

Institute of Technology Engine Dimensions 605 

Intercooler 721 

Investigation, Method of 2 

Involution by Diagram 20 

Isothermal, Definition 342 

' ' Expansion of Gases 711 

j 

Johnson's Extensometer 129 

Jolly Air -thermometer 373 

Journal Friction 198 

Jump-spark Ignition 705 

K 

Kellogg Testing Machine 93 

Kent Calorimeter 409 

Kent's Draft Gauge . . 355 

Knife-edge of Testing Machine 95 

L 

Latent Heat of Steam 34! 

" Table of 788 

Lazy Tongs 532 

Leakage of Boilers, Locomotive Tests 648 

' ' Test of Pumps 622 

Leaks, Test for, in Engine 582 

Least Squares 5 

Le Chatelier Specific Gravity Apparatus 183 

Lenoir Gas-engine 701 

Lewis Dynamometer 252 

Lime, definition of x 8i 

Limits of Throttling -calorimeter 429 

Linde Ice-machine Test 748 

Lloyd's Tests for Steel x y- 

Load Variation Diagram 564 

Locomotive Boiler Test. 6™ 

Coal Tests 642 



826 



INDEX, 



PAGE 

Locomotive Test, Object 634 

" Standard Method 634 

' ' Water Measurement 645 

1 ' Tests, Form for 653 

" " General Results 654 

1 * " Speed Recorder 650 

" Staff for 652 

Logarithm Table, Use of 64 

Logarithms, Common Table of 769 

Hyperbolic, " " 784 

Logarithmic Paper 23 

Lubricants, Durability Test 226 

Lubricant Testing 201 

Lubricated Surfaces, Friction of 201 

M 

McNaught's Steam-engine Indicator 517 

Machinery, Hydraulic, Classification 308 

Machines for Computation 64 

Mack Non-lifting Injector 670 

Mahler's Fuel Calorimeter .' 461 

Maillard Testing Machine . 94 

Manographie 525 

Manometer 345 

1 ' Cistern Form 347 

1 ' U-shaped 345 

Marshall Extensometer j^j 

Materials, Strength of, Table 781 

Material Tests 67 

Mean Effective Pressure 550 

M.E.P., Table for Equivalent H.P 800 

Mean Error 7 

' ' Ordinate, Length of 22 

Measurement of Feed-water 616 

Mechanical Efficiency 569 

" " How Computed 628 

1 ' Equivalent of Heat 330 

Mercurial Thermometer. 369 

1 ' Weight Thermometer 370 

Mercury Column, Calibration of Gauges 366 

" ' " Useof 351 



INDEX. 827 



PAGE 



Mercury Columns 349 

" Table of Depression 350 

Metal, Strength of, at Different Temperatures ~. . . . 782 

Metals, Table of Specific Gravity. 783 

" Table of Specific Heat 783 

Metallic Pyrometer 381 

Meter, Gas 303 

1 1 Prover 304 

Meters for Water 283 

Method of Taking Indicator Diagrams 544 

Metric Measures, Table of 754 

Micrometer 50 

1 ' Caliper 59 

Mirror Extensometer 125 

Mistakes, Rejection of 71 

Modulus of Elasticity 73 

" ''Rigidity 83 

Moisture Absorbed by Air, Table 785 

Moment of Flexure 76 

Moments, External, Table 79 

" of Inertia 80 

" " " Table 78 

Morin Dynamometer 247 

Calibration 249 

Morse Thermal Heat Gauge 386 

Mortar 182 

Moscrop Speed-recorder 577 

Moulds for Cement 141 

Multiplying Draft Gauges 355 

N 

Naperian Logarithms, Table of 784 

Napier's Formula, Table of Discharge of Steam 795 

Necking of Test Specimen 143 

Needle, Vicat 186 

Noel's Optical Pyrometer 386 

Normal Consistency Test. 185 

Nozzle Calibration 287 

' ' Discharge, DeLaval Turbine 688 

Nozzles, Discharge Through 275 

Numerical Calculations, Accuracy of 19 

1 ' Constants, Table of 756 



828 



INDEX. 



O 



Oil Adulteration 202 

Density . 202 

Engines 709 

Test for Acids 215 

' ' Burning-point 212 

1 ' Durability 226 

1 ' Evaporation 212 

Flash 210 

Forms 233 

for Freezing 213 

' ' Gumming 210 

with Limited Feed 231 

of Viscosity 204 

Testing 201 

' ' Machine, Ashcroft's 227 

' ' Boult's 227 

' ' Directions 222 

R.R 218 

" Riehle's 224 

" Theory '. 220 

" Thurston's 217 

" Machines. 215 

Oleography 214 

Olsen Autographic Apparatus in 

' ' Cement Machine 121 

" Testing Machine 92,110 

' ' Torsion Machine 188a 

Optical Indicator 525 

' ' Pyrometers 386 

Ordinate, Mean 22 

Orsat's Flue -gas Apparatus 482 

Otto Cycle 702 

Otto & Langen Gas-engine 701 

Overshot Water-wheels 311 

Oxygen Absorbents 475 

' ' Method of Measuring Heating Value 446 



INDEX. 829 

P 



PAGE 



Paine Extensometer 127 

Pantograph 531 

Paper Drum for Indicators 529 

' ' Logarithmic 23 

Parsons' Steam-turbine 689 

Paving Materials, Test of 179 

Peabody Calorimeter 419 

Peclet's Draft-gauge 353 

Pelton Motor, Test of 324 

' ' Water-wheel 315 

Pencil Mechanism of Indicator. 526 

' ' Movement on Indicator, Test of 539 

Pendulum Reducing Motion 530 

' ' Viscosometer 209 

Pennsylvania R.R. Viscosometer 204 

Perfect Engine Efficiency 570 

Perkins Viscosometer 205 

Phcenix Testing-machine 93 

Phosphorus 475 

' ' Determination of 470 

Pillow-block Dynamometer 252 

Pipe-fitting Calorimeter for Steam 422 

Pipes, Flow Through 277 

Pipe, Table of Standard Dimensions 798 

Piston Air-compressor 720 

' ' Displacement, how measured 583 

Pitot Tube 292 

" " for High Pressures 294 

" " Use of, for Measuring Air 726 

Pivot Friction IQ 8 

Planimeter Adjustment 50 

Calibration •. 52, 780 

Directions $j 

Errors 55 

' ' Measurement of Diagrams ^ z 

Roller 45 

' ' Suspended 4I 

Plant Efficiency ^ 70 

Platinum Ball Pyrometer. . .' 38^ 

Polar Planimeter 30 

Theory 32 



830 INDEX. 

PAGE 

Portland Cement, Definition jgj 

1 ' " Specifications 192 

" Testing l82 

Potassium Pyrogallate 475 

Power-pumps, Tests of 031 

' ' Systems Testing Machines 89 

Pressure of Atmosphere 336 

' ' by Gauge 336 

' ' Measured by Manometer 347 

Units, Table of 336 

" and Volume, Formulae for Compression of Gas 711 

" Relations of, in Refrigeration 744 

Preston Air-thermometer 372 

Priestman Oil-engine , 710 

Probable Error 7 

Probability of Errors 6 

Products of Combustion, Object of Analysis 473 

Prony Brake 235 

" " Designing 236 

' ' " Directions 244 

1 ' " for Engine -testing 582 

* i Brakes, Various Forms 239 

Properties of Steam , 340 

Pulsometer, Description of 683 

' ' Form for Tests 684 

Theory of 684 

Pump Brake 245 

1 - Test, Computation and Results 628 

' ' Forms for 332 

1 ' Form of Report 624 

Pumps, Centrifugal, Test of 331 

' l Classification of .' 327 

1 ' Duty and Capacity of 328 

1 c Efficiency Test 330 

' ' Measurement of Work 329 

' ' Rotary 328 

" sli P of 330 

Pumping-engine, Leakage Test 622 

1 ' Observations 620 

Pumping-engines, Duty Trial 618 

Punching Test 166 

Puzzuolana 182 



INDEX. 83 1 



PAGE 



Pyrometer Calibration 780 

' ' for Locomotive -testing 641 

Pyrometers 380 

' ' Comparison of 389 

Q 

Quality of Steam, Definition 390 

" " Duty Test 621 

" " Formula for 393 

' ' " " Methods of Determining 394 

' ' tl " from Saturation Curve 610 

R 

Ram, Hydraulic 32r 

Rankine's Formula 74 

' ' Oil-testing Machine 215 

Reaction Steam-turbine 689 

" Turbine 316 

1 ' Water-wheel 319 

Recording Gauges 361 

Records of Boiler-test 501 

Rectangular Weir 272 

Reducing Motion for Indicators 529 

" " " Locomotives 637 

" Test of 579 

1 ' Wheels 532 

' ' Wheel for Indicator ... 524 

Re -evaporation 561 

Refrigerating Machine of Air 741 

" " Ammonia 742 

Defined 734 

" " Efficiency 736 

11 " Heat Exchanges 735 

M tl Ideal Efficiency 735 

li " Negative Heat Losses 738 

11 Test 748 

" Plant, Illustrated 746 

Refrigeration, Absorption System 747 

' ' Data and Result Sheets 749 

Regenerator Hot-air Engine 695 

Relation of Pressure and Temperature of Gases 712 



832 INDEX. 



PAGE 



Report, Form of 3 

' ' of Test, Steam-turbine. 693 

Residual 7 

Resilience 6& 

' ' Torsional 83 

Revolution-counter ^ 2 

Richards's Indicator q x g 

Rider Hot-air Engine 695 

" Method of Operating 7 oo 

Riehle Cement Machine I2 2 

' ' Extensometer I2 8 

' ' Hydraulic Machine IO y 

1 1 Oil-testing Machine 224 

' ' Power Machine 108 

1 ' Testing Machine g Z 

' ' Torsion Machine ug 

Rigidity 68 

' ' Modulus of Wire 83 

Roller Planimeter 45 

Rope Test-piece 140 

Rotary Pumps 328 

Rubber, Effects of Strain 86 



S 

Sample of Steam for Calorimeter 399 

Sampling of Flue-gas 477 

" Fuel -....* 452 

Sand, Standard 187 

Saturation Curve, Formula for 555 

" " Heat Analysis from 609 

" " Heat Interchanges from 611 

Screws, Micrometer 50 

Seaman's Pyrometer 385 

Sellers's Injector 671 

Separating Calorimeter 43a 

" ' ' Forms 439 

Formula 436 

" " Table of Accuracy 431 

" " Various forms 432 

Setting of Cement 192 

" " Valves of Steam Engine 586 



INDEX. 833 



Shaft Diagram 567 

Shafting, Table of H.P 804 

Shear, Parallel 77 

Shearing Strain, Theory 81 

" and Normal Stress 84 

Sibley College Experimental Engine, Dimensions 657 

Sieves for Cement 184 

Signs and Tangents, Table of 777 

Simple-lever Machines 90 

Slide-rule, description 24 

* ' Directions 25 

Fuller's 28 

" Thatcher's 27 

Slip of Pumps 330 

Smoke Observations in Boiler-testing 505 

Specifications Bridge Material 169 

for Cement 190 

of Eye-bars 171 

' Iron Plate 172 

' for Steel, Lloyd's 173 

' Steel Plate 172 

1 Water-pipe 1 74 

Specific Gravity of Cement required 191 

" " Metals, Table of 783 

' ' Table corresponding to Beaume's Scale 786 

" " Test of Cement 183 

Specific Heat, definition ^8 

" ' ' of Brine 752 

' * " Chloride of Calcium 752 

" " Determination ' 382 

" " of i ? uel-gases, Table 450 

"of Metals, Table of , 783 

" " and Melting-point, Tables of 383 

Speed-counter 571 

Speed-indicator 571 

" Calibration 579 

Speed Measurement with Chronograph 573 

• " Tachometer 572 

Speed-recorder, Locomotive Tests 650 

Square-inch Gauge-testing Apparatus 365 

Squares and Diameter, Table of 576 

Standard Form Test-pieces 136 



834 INDEX. 



Standard Method of Testing Boilers 4Q - 

" " " Cement j8 2 

" " " Locomotive Testing 634 

1 1 Test of Pumping -engines 614 

Steam-boiler Test Definitions 403 

Steam-boilers, Object of Test 492 

Steam Calorimeter for Locomotive Tests 655 

Steam Calorimeters, Classification 391 

Steam-chest Diagram 567 

Steam Accounted for by Indicator, References to Tables 560 

" Density and Specific Volume Formula 342 

' ' Dry and Saturated 340 

1 ' Flow of, Through Orifice 300 

1 ' Formula for Heat, Contents 393 

" " Quality... 393 

" Fuel- and Heat- consumption, of Engine Definitions 569 

" per I.H.P. from Indicator-diagram 558 

' ' Measurement of Heat, Contents 394 

1 ' Methods of Determining Quality 394 

1 i Properties of 340 

1 ' Quality of, Definition 390 

" Relations of Pressure and Temperature 339 

' ' Sample for Calorimeter 391 

1 ' Superheated Properties 340 

1 ' Table of Entropy 301, 794 

" Table of Properties 788 

1 ' Weight Discharged Through Orifice 302 

Steam-engine Clearance, how measured 583 

' ' Compound, Test of 631 

1 ' Efficiency Test 589 

" Indicator 515 

" * ' Care of 545 

" " Early Forms 517 

Ci " for Locomotives 638 

" " Parts 526 

u Inertia of Parts 660 

Methods of Testing 581 

Optical Indicator 525 

References. 325 

Terms Defined 569 

Test for Friction 589 

Test, Hirn's Analysis 590 



INDEX. 835 



PAGE 



Steam-engine Valve-setting 586 

Steam-engines, Water- consumption Tables. 802 

Steam Gauges 357 

Steam-gauge Calibration 579 

Steam-injector, Description ; 670 

1 ' Directions for Handling and Applying 679 

" Testing 679 

1 ' Form for Data and Results 681 

' ' Limit of Suction-head 678 

1 ' Limits of Capacity 676 

" "of Temperature 677 

1 ' Mechanical Theory 674 

Theory of 672 

Steam Pumping-engines, Standard Test of 614 

Steam-separator, Use of 615 

Steam Tables 340 

' ' " Compared 344 

" Use of 392 

Steam-turbine, Description of 686 

' ' Testing 691 

Steelyard Dynamometer 250 

Stillman's Viscosometer 206 

Stones, Frost Test 1 76 

" Tests of 175 

Straight Line Indicator 525 

" Lyne " 525 

Strain, Definition of 68 

1 ' Diagram Torsion Machine n6 

' ' Diagrams 69, 144 

" " Autographic 145 

" Relation to Temperature 86 

Strap-brakes 240 

Strength at High Temperature 167 

' ' of Materials, Notation 72 

" " Table of Coefficients 781 

Strengths after Repeated Applications of Load 167 

Stress, Definition 67 

' ' Twisting with Bending 85 

" " " Longitudinal 84 

Stresses, Brake -strap 236 

' ' Combination of 84 

Strohmyer's Extensometer I2 6 



836 INDEX. 



PAGE 



Sulphur, Determination of, in Coal 470 

Superheating Calorimeters 398 

Surface Condenser 576 

Suspended Planimeter , 4I 

Sweet Measuring-machine 60 

Swelling Test of Cement jg 2 



T 

Table, Air, Moisture Absorbed by 785 

" Angles, Natural Functions of 777 

1 ' Analysis of Ash 787 

' * Anhydrous Ammonia, Properties of 740 

Beaume Hydrometer Scale 786 

of Boiling-points 423 

Chemical Equivalents 444 

Coefficients of Friction 784 

Strength 781 

Composition of Fuels 451 

Fuels of U. S 787 

■■•- 703 

' ' ' ' Depression, Mercury Column 350 

1 ' Dimensions of Wrought-iron Pipe 798 

" Discharge of Steam by Napier's Formula 795 

1 ' Entropy of Steam. 301 

' ' Errors in Calorimeters 397 

' ' External Moments 79 

' ' Factors of Evaporation 797 

1 ' Heat of Combustion 446 

' ' Horse-power of Belting 804 

per Pound M.E.P 800 

" " of Shafting 804 

1 ' Humidity of the Air 785 

' ' Hyperbolic Logarithms 784 

1 1 Indicator Dimensions 528 

1 1 Logarithmic Functions of Angles 771 

Logarithms 759 

Materials, Important Properties of 783 

Maximum Temperature of Combustion 450 



tt 

ci a 

11 (i 

<( tt a 

(t ic 



" " " " Gases. 



tt 



tt 

" of Feed-water for Injector 678 



tt 



Moisture Absorbed by Air 785 

Moments of Inertia 78 



INDEX. 



837 



Table of Numerical Constants 756 

Pressure, Units of 336 

Specific Heat of Gases 450 

Specific Heat and Melting-points 383 

Specific Heat of Water ^8 

Steam -injector, Limits of 677 

Steam, Properties of .' 788 

Strength of Metal at Different Temperatures. . 782 

Suction-head, Limit of, in Injector 678 

Thermometric Scales .' 337 

Throttling-calorimeter, Limits of 429 

Throttling-calorimeter, Application 795 

Transverse Loads 78 

U. S. Standard and Metric Weights 754 

Water, Density and Weight of 799 

Water Consumption for Steam-engines 802 

Weir Discharge 803 

Tabor Indicator 520 

' ' External Spring 524 

Tachometer for Measuring Speed 572 

' ' Water Measurements 290 

Tagliabue Viscosometer 205 

Temperature 342 

Produced by Combustion 448 

Effect on Strength 167 

Maximum, Table of 450 

Measured by Hot Body 381 

Measurement of Steam 400 

Relation to Heat 337 

" Strain 86 

Rise in Adiabatic Compression 729 

Temperatures of Feed-water, How found 615 

Tension, Specimen Gauge 147 

Tensile Strength, Cement 192 

Formula 72 

Tension Test, Blank 150 

1 ' Directions 145, 149 

" Forms 152 

" Necking I43 

" Piece 137,138 

" Report I49 

Test by Abrasion T 66 



838 



INDEX. 



PAG E 

Test, Admiralty, for Iron Plate 172 

" Steel Plate 172 

of Asphalt 180 

by Bending 166 

of Bricks 178 

' ' Bridge Materials 168 

" Car Wheels 167 

' ' Cement 182 

' ' Compound Pumping-engine 631 

1 ' Condenser 578 

' ' Density 203 

by Drop Method 164 

of Efficiency 3 

by Forging 166 

of Belts 263 

1 ' Gas- or Oil-engines 714 

" Gauges 363 

by Hammer 166 

' ' Hardening 166 

of Hot-air Engine 697 

by Impact, Directions 163 

of Injector 679 

' ' Lubricants 201 

" Materials 67 

' ' Paving Materials. 171 

' ' Power-pumps 339 

' ' Pulsometer 684 

' ' Refrigerating-machine 748 

by Repeated Loading 166 

of Specific Gravity of Cement 183 

1 ' Steam-turbines 691 

' ' Stones . m 175 

1 ' Torsion, Long Specimens 118& 

' ' Viscosity 204 

' ' Water-pipe 1 74 

Test-pieces, Cast-iron 139 

' ' Cement 140 

1 i Chain 139 

' ' Compression 142 

' ' Form of 136 

Rope ! 140 

" Tension 138 






INDEX. 839 



u 



and Lever. 



PAGE 

Test-pieces, Torsion 142 

Transverse 142 

" of Wire-rope 140 

" " Wood 138 

Testing of Water-motors 322 

" by Welding z 6$ 

Testing-machine, Calibration 97 

Cement 119 

Classification 90 

Compound Lever 91 

Differential Lever 91 

Emery 102 

Extensometer 124 

Frame 97 

Fulcrum 95 

Hydraulic 92 

93 

Impact and Drop 119 

" Olsen IIO 

Power System 89, 98 

Requirements of 88 

" Riehle, Hydraulic 107 

" Power 108 

" Shackle's 89, 98 

Simple-lever 90 

Torsion, Thurston 114 

Varieties and Forms 88 

Watertown Arsenal 100 

Wedges 100 

Weighing Devices 88 

Weighing System 96 

Thatcher's Slide-rule 27 

Theory, Hot-air Engine 697 

Thermodynamic Efficiency 570 

Thermometers, Air 371 

Thermometer, Alcohol 371 

Calibration 380, 580 

Cups 400 

" Mercurial 369 

Rules for Handling 370 

Thermometric Scales, Table of 337 

Thompson's Fuel Calorimeter 455 



840 INDEX, 



Thompson Indicator 519 

Three-way Cock ... 544 

Throttling-calorimeter ; 398, 418 

" Diagram 425 

" " for use 796 

" Forms 430 

' ' Limit of 427 

' ' Table for use 795 

Thurston Extensometer 129 

Thurston's Oil-testing Machine, Directions 222 

Standard 217 

Theory 220 

" R.R. Oil-testing Machine 219 

' ' Torsion-machine 114 

" " Diagram 115 

" " Directions 161 

Torsion-machine Thurston 114 

" Olsen n8fl 

" Riehle 117, n 8 

Torsion Strain, Theory 82 

Torsion-test, Directions 160 

Forms for Report 162 

Torsion Testing-machine 114 

Torsion-tests, Long Specimens 1186 

Torsion Test-pieces '. 142 

Torsional Resilience 8^ 

Traction Dynamometer 246 

Transmission Dynamometer 247 

Transverse Deflectometer 135 

' ' Formula 76 

' ' Loads, Table 78 

' ' Test, Directions 156 

" ' ' Elastic Curve 159 

" " Forms 157 

' ' Specimens 142 

Trapezoidal Weir 272 

Triangular Weir 272 

Triple-engine, Hirn's Analysis 604 

Triple -expansion, Diagrams. 565 

Tuning-fork Chronograph 574 

Turbine, Steam-, Description of 686 

Water-wheel 315 



INDEX. 84I 



PAGE 



Turbine, Water-wheel, Forms of Test 318 

Theory , 316 

Twisting and Bending Stress 85 

' ' ' ' Longitudinal Stress 84 

Two-cycle Gas-engine 707 



U 

Undershot Water-wheels 313 

Unwin's Extensometer 126 

U-shaped Manometer 345 

V 

Vacuum Gauge 360 

" " Calibration 367 

Vacuum Line 548 

Valve-setting 586 

Valves, Loss of Head 279 

Van Winkle Power-meter 261 

Variation of Load, Diagram 564 

Velocity of Approach 283 

' ' " Discharge, Coefficient for 271 

' ' ' ' Flow of Air ; . . 297 

" Head 271 

' ' of Nozzle Discharge, DeLaval Turbine 688 

Venturi Tube Calibration 287 

' ' Flow Through 275 

Vernier 29 

" Caliper 57 

Vicat Needle 186 

Viscosity of Materials 70 

" " Metals 167 

" Oil 203 

' ' Test, Directions 208 

Viscosbmeter, Carpenter's 207 

Gibbs's 205 

' ' Pendulum. 209 

Pennsylvania R.R 204 

Perkins 205 

Stillman 206 

' ' Tagliabue 205 



842 



INDEX. 



; PAGE 

Volume of Air Discharged 296 

" " " Measured by Heat absorbed 727 

W 

Water, Computation Table for Steam-engine 802 

' ' Energy of Falling 309 

' ' Equivalent of Calorimeter 401 

' ' Flow in Circular Pipes 277 

" " through Nozzles 275 

' ' under Pressure 276 

" "in Streams, Measurement of 289 

" ll through Venturi Tubes 275 

' ' ' ' over Weirs 272, 281 

' ' Measurement of Flow 281 

" " in Pipes 288 

" with Pitot's Tube 292 

' ' Measurement of Head 281 

' ' Measurement with Hydrometric Pendulum 295 

' ' Measurements, Locomotive Tests 645 

' ' Meters 283 

1 - Meter Calibration 579 

" Errors . 284 

1 ' Locomotive Test 64, 645 

' ' Motors, Measurement of Head 323 

Testing of: 322 

' ' Table of, Density and Weight 799 

' ' Theory of Flow 270 

Water-pipe Specifications 174 

Water-pressure Engines \ 309 

" Test of 325 

Water-power System, Parts of 309 

Water Ram 321 

Water- vapor for Refrigeration 739 

Water-wheels, Breast 313 

Classified 310 

" Impulse 314 

Overshot 311 

Poncelet 314 

' ' Reaction Type 319 

Water-wheels, Test of 325 

' ' Turbines , 315 

Undershot 313 



INDEX. 843 

PAGE 

Watertown Testing-machine 100 

Watt Steam-engine Indicator '. ^7 

Wearing-test Paving-brick x 8o 

Weathering Quality of Stone 178 

Webber Dynamometer 255 

Wedge Extensometer 124 

Wedgewood's Pyrometer 381 

Weighing Device, Testing-machines 88 

Scales Calibration 579 

System Testing-machine. 96 

Weight of Steam from Indicator Diagram. . 557 

Weir Calibration 285 

Weirs, Coefficients for 274 

Different Forms 272 ' 

Discharge over, Table of 803 

Formula for 273 

Measurement of Water, Errors in 282 

Measurement of Head 281 

Requirements for Accuracy 282 

Welding Test 165 

Welter's Method of Measuring Heating Value 446 

Werder Testing-machine 93 

Westinghouse Gas-engine 706 

Williams's Inertia Indicator 661 

Willis's Planimeter 45 

Wilson's Flue -gas Apparatus 481 

Wind Resistance, Locomotive Tests 651 

Wipe Spark-ignition 704 

Wire-drawing 550 

Wire -rope Test-piece 140 

Wooden Tension Test-pieces 138 

Work -diagram 21 

Work Lost due to Heating in Compression 729 

' * Mechanical, Isothermal Expansion 712 

Y 

Yield Point 69 

Z 

Zero Absolute 338 

" Circle, Theory 3 g 

Zeuner's Valve-diagram 587 



SHORT-TITLE CATALOGUE 

OF THE 

PUBLICATIONS 

OF 

JOHN WILEY & SONS, 

New York. 
London: CHAPMAN & HALL, Limited. 



ARRANGED UNDER SUBJECTS. 



Descriptive circulars sent on application. Books marked with an asterisk (*) are sold 
at net prices only, a double asterisk (**) books sold under the rules of the American 
Publishers' Association at net prices subject to an extra charge for postage. All books 
are bound in cloth unless otherwise stated. 



AGRICULTURE. 

Armsby's Manual of Cattle-feeding i2mo, $i 75 

Principles of Animal Nutrition 8vo, 4 00 

Budd and Hansen's American Horticultural Manual: 

Part I. Propagation, Culture, and Improvement i2mo, 1 50 

Part II. Systematic Pomology nmo, 1 .50 

Downing's Fruits and Fruit-trees of America 8vo, 5 00 

Elliott's Engineering for Land Drainage i2mo, 1 50 

Practical Farm Drainage nmo, 1 00 

Green's Principles of American Forestry i2mo, 1 50 

Grotenfelt's Principles of Modern Dairy Practice. (Woll.) i2mo, 2 00 

Kemp's Landscape Gardening nmo, 2 50 

Maynard's Landscape Gardening as Applied to Home Decoration i2mo, 1 50 

* McKay and Larsen's Principles and Practice of Butter-making 8vo, 1 50 

Sanderson's Insects Injurious to Staple Crops i2mo, 1 50 

Insects Injurious to Garden Crops. (In preparation.) 
Insects Injuring Fruits. (In preparation.) 

Stockbridge's Rocks and Soils 8vo, 2 50 

Winton's Microscopy of Vegetable Foods 8vo, 7 50 

Woll's Handbook for Farmers and Dairymen i6mo, 1 50 

ARCHITECTURE. 

Baldwin's Steam Heating for Buildings i2mo, 2 50 

Bashore's Sanitation of a Country House i2mo, 1 00 

Berg's Buildings and Structures of American Eailroads 410, 5 00 

Birkmire's Planning and Construction of American Theatres. . . 8vo, 3 00 

Architectural Iron and Steel 8vo, 3 50 

Compound Riveted Girders as Applied in Buildings 8vo, 2 00 

Planning and Construction of High Office Buildings 8vo, 3 50 

Skeleton Construction in Buildings 8vo, 3 00 

Brigg's Modern American School Buildings 8vo, 4 00 

Carpenter's Heating and Ventilating of Buildings 8vo, 4 00 

Freitag's Architectural Engineering 8vo, 3 50 

Fireproofing of Steel Buildings 8vo, 2 50 

French and Ives's Stereotomy 8vo, 2 50 

1 



Gerhard's Guide to Sanitary House-inspection i6mo, 

Theatre Fires and Panics i2mo, 

♦Greene's Structural Mechanics 8vo, 

Holly's Carpenters' and Joiners' Handbook i8mo, 

Johnson's Statics by Algebraic and Graphic Methods 8vo, 

Kidder's Architects' and Builders' Pocket-book. Rewritten Edition. i6mo, mor., 

Merrill's Stones for Building and Decoration 8vo, 

Non-metallic Minerals: Their Occurrence and Uses 8vo, 

Monckton's Stair-building 4to, 

Patton's Practical Treatise on Foundations 8vo, 

Peabody's Naval Architecture 8vo, 

Richey's Handbook for Superintendents of Construction i6mo, mor., 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 

Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, 

Snow's Principal Species of Wood 8vo, 

Sondericker's Graphic Statics with Applications to Trusses, Beams, and Arches. 

8vo, 

Towne's Locks and Builders' Hardware i8mo, morocco, 

Wait's Engineering and Architectural Jurisprudence 8vo, 

Sheep, 
Law of Operations Preliminary to Construction in Engineering and Archi- 
tecture 8vo, 

Sheep, 

Law of Contracts. . ., 8vo, 

Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. 8vo, 

Worcester and Atkinson's Small Hospitals, Establishment and Maintenance, 

Suggestions for Hospital Architecture, with Plans for a Small Hospital. 

i2mo, 
The World's Columbian Exposition of 1893 Large 4to, 



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ARMY AND NAVY. 



Bernadou's Smokeless Powder, Nitro-cellulose, and the Theory of the Cellulose 

Molecule i2mo, 2 50 

* Bruff's Text-book Ordnance and Gunnery 8vo, 6 00 

Chase's Screw Propellers and Marine Propulsion 8vo, 3 00 

Cloke's Gunner's Examiner 8vo, 1 50 

Craig's Azimuth . . 4to, 3 50 

Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 00 

* Davis's Elements of Law 8vo, 2 50 

* Treatise on the Military Law of United States 8vo, 7 00 

Sheep, 7 50 

De Brack's Cavalry Outposts Duties. (Carr.) : 24mo, morocco, 2 00 

Dietz's Soldier's First Aid Handbook i6mo, morocco, 1 25 

* Dredge's Modern French Artillery 410, half morocco, 15 00 

Durand's Resistance and Propulsion of Ships. . .' 8vo, 5 00 

* Dyer's Handbook of Light Artillery nmo, 3 00 

Eissler's Modern High Explosives 8vo, 4 00 

* Fiebeger's Text-book on Field Fortification Small 8vo, 2 00 

Hamilton's The Gunner's Catechism i8mo, 1 00 

* Hoff's Elementary Naval Tactics 8vo, 1 50 

Ingalls's Handbook of Problems in Direct Fire 8vo, 4 00 

* Ballistic Tables 8vo, 1 50 

* Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and II. .8vo, each, 6 00 

* Mahan's Permanent Fortifications. (Mercur.) 8vo, half morocco, 7 50 

Manual for Courts-martial i6mo, morocco, 1 50 

* Mercur's Attack of Fortified Places i2mo, 2 00 

* Elements of the Art of War 8vo, 4 00 

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Metcalf's Cost of Manufactures — And the Administration of Workshops. .8vo, 

* Ordnance and Gunnery. 2 vols. nmo, 

Murray's Infantry Drill Regulations i8mo, paper, 

Nixon's Adjutants' Manual 24010, 

Peabody's Naval Architecture 8vo, 

* Phelps's Practical Marina Surveying 8vo, 

Powell's Army Officer's Examiner nmo, 

Sharpe's Art of Subsisting Armies in War i8mo, morocco 

* Tupes and Poole's Manual of Bayonet Exercises and Musketry Fencing. 

241110, leather, 

* Walke's Lectures on Explosives 8vo, 

* Wheeler's Siege Operations and Military Mining 8vo, 

Winthrop's Abridgment of Military Law i2mo, 

Woodhull's Notes on Military Hygiene i6mo, 

Young's Simple Elements of Navigation i6mo, morocco, 

ASSAYING. 

Fletcher's Practical Instructions in Quantitative Assaying with the Blowpipe. 

nmo, morocco, 1 50 

Furman's Manual of Practical Assaying 8vo, 3 00 

Lodge's Notes on Assaying and Metallurgical Laboratory Experiments .... 8vo, 3 00 

Low's Technical Methods of Ore Analysis 1 8vo, 3 00 

Miller's Manual of Assaying nmo, 1 00 

Minet's Production of Aluminum and its Industrial Use. (Waldo.) nmo, 2 50 

O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 2 00 

Ricketts and Miller's Notes on Assaying 8vo, 3 00 

Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 4 00 

Ulke's Modern Electrolytic Copper Refining 8vo, 3 00 

Wilson's Cyanide Processes nmo, 1 50 

Chlorination Process nmo, 1 50 

ASTRONOMY. 

Comstock's Field Astronomy for Engineers 8vo, 2 50 

Craig's Azimuth 4to, 3 50 

Doolittle's Treatise on Practical Astronomy 8vo, 4 00 

Gore's Elements of Geodesy 8vo, 2 " 50 

Hayford's Text-book of Geodetic Astronomy 8vo, 3 00 

Merriman's Elements of Precise Surveying and Geodesy 8vo, 2 50 

* Michie and Harlow's Practical Astronomy 8vo, 3 00 

* White's Elements of Theoretical and Descriptive Astronomy nmo, 2 00 

BOTANY. 

Davenport's Statistical Methods, with Special Reference to Biological Variation. 

i6mo, morocco, 1 25 

Thome and Bennett's Structural and Physiological Botany i6mo, 2 25 

Westermaier's Compendium of General Botany. (Schneider.). . . , 8vo, 2 00 

CHEMISTRY. 

Adriance's Laboratory Calculations and Specific Gravity Tables nmo, 1 25 

Allen's Tables for Iron Analysis 8vo, 3 00 

Arnold's Compendium of Chemistry. (Mandel.) Small 8vo, 3 50 

Austen's Notes for Chemical Students nmo, 1 50 

Bernadou's Smokeless Powder. — Nitro-cellulose, and Theory of the Cellulose 

Molecule > nmo, 2 50 

* Browning's Introduction to the Rarer Elements 8vo, 1 50 

3 



Brush and Penfield's Manual of Determinative Mineralogy ivo, 

Classen's Quantitative Chemical Analysis by Electrolysis. (Eoltwcod.). . 8vo, 

Cohn's Indicators and Test-papers nmo, 

Tests and Reagents 8vo, 

Crafts's Short Course in Qualitative Chemical Analysis. (Schaeffer.). . . nmo, 
Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von 

Ende.) nmo, 

Drechsel's Chemical Reactions. (Merrill.) i2mo, 

Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 

Eissler's Modern High Explosives 8vo, 

Effront's Enzymes and their Applications. (Prescott.) 8vo> 

Erdmann's Introduction to Chemical Preparations. (Dunlap.) nmo, 

Fletcher's Practical Instructions in Quantitative Assaying with the Blowpipe. 

nmo, morocco, 

Fowler's Sewage Works Analyses nmo, 

Fresenius's Manual of Qualitative Chemical Analysis. (Wells.) 8vo, 

Manual of Qualitative Chemical Analysis. Parti. Descriptive. (Wells.) 8vo, 
System of Instruction in Quantitative Chemical Analysis. (Cohn.) 

2 vols 8vo, 

Fuertes's Water and Public Health nmo, 

Furman's Manual of Practical Assaying 8vo, 

* Getman's Exercises in Physical Chemistry nmo, 

Gill's Gas and Fuel Analysis for Engineers nmo, 

Grotenfelt's Principles of Modern Dairy Practice. (Woll.) nmo, 

Hammarsten's Text-book of Physiological Chemistry. (Mandel.) 8vo, 

Helm's Principles of Mathematical Chemistry. (Morgan.) nmo, 

Hering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 

Hind's Inorganic Chemistry 8vo, 

* Laboratory Manual for Students nmo, 

Holleman's Text-book of Inorganic Chemistry. (Cooper.) 8vo, 

Text-book of Organic Chemistry. (Walker and Mott.) 8vo, 

* Laboratory Manual of Organic Chemistry. (Walker.) nmo, 

Hopkins's Oil-chemists' Handbook 8vo, 

Jackson's Directions for Laboratory Work in Physiological Chemistry. .8vo, 

Keep's Cast Iron 8vo, 

Ladd's Manual of Quantitative Chemical Analysis nmo, 

Landauer's Spectrum Analysis. (Tingle.) 8vo, 

* Langworthy and Austen. The Occurrence of Aluminium in Vege able 

Products, Animal Products, and Natural Waters 8vo, 

Lassar-Cohn's Practical Urinary Analysis. (Lorenz.) nmo, 

Application of Some General Reactions to Investigations in Organic 

Chemistry. (Tingle. ) nmo, 

Leach's The Inspection and Analysis of Food with Special Reference to State 

Control." 8vo, 

Lob's Electrochemistry of Organic Compounds. (Lorenz.) 8vo, 

Lodge's Notes on Assaying and Metallurgical Laboratory Experiments. .. .8vo, 

Low's Technical Method of Ore Analysis 8vo, 

Lunge's Techno-chemical Analysis. (Cohn.) nmo 

* McKay and Larsen's Principles and Practice of Butter-making 8vo. 

Mandel's Handbook for Bio-chemical Laboratory nmo, 

* Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe. . nmo, 
Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 

3d Edition, Rewritten 8vo, 

Examination of Water. (Chemical and Bacteriological.) nmo, 

Matthew's The Textile Fibres 8vo, 

Meyer's Determination of Radicles in Carbon Compounds. (Tingle.), .nmo, 

Miller's Manual of Assaying nmo, 

Minet's Production of Aluminum and its Industrial Use. (Waldo.) . . . . nmo, 

Mixter's Elementary Text-book of Chemistry nmo, 

Morgan's An Outline of the Theory of Solutions and its Results nmo, 

4 



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Morgan's Elements of Physical Chemistry i2mo, 

* Physical Chemistry for Electrical Engineers i2mo, 

Morse's Calculations used in Cane-sugar Factories i6mo, morocco, 

Mulliken's General Method for the Identification of Pure Organic Compounds. 

Vol. I Large 8vo, 

O'Brine's Laboratory Guide in Chemical Analysis 8vo, 

O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 

Ostwald's Conversations on Chemistry. Part One. (Ramsey.) i2mo, 

" " " Part Two. (Turnbull.) i2mo, 

* Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests. 

8vo, paper, 

Pictet's The Alkaloids and their Chemical Constitution. (Biddle.) 8vo, 

Pinner's Introduction to Organic Chemistry. (Austen.) i2mo, 

Poole's Calorific Power of Fuels. . 8vo, 

Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- 
ence to Saaitary Water Analysis ' i2mo, 

* Reisig's Guide to Piece-dyeing 8vo, 

Richards and Woodman's Air, Water, and Food from a Sanitary Stand- 
point 8vo, 

Ricketts and Russell's Skeleton Notes upon Inorganic Chemistry. (Part I. 

Non-metallic Elements.) 8vo, morocco, 

Ricketts and Miller's Notes on Assaying 8vo, 

Rideal's Sewage and the Bacterial Purification of Sewage. . 8vo, 

Disinfection and the Preservation of Food 8vo, 

Riggs's Elementary Manual for the Chemical Laboratory 8vo, 

Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 

Rostoski's Serum Diagnosis. (Bolduan.) i2mo, 

Ruddiman's Incompatibilities in Prescriptions 8vo, 

* Whys in Pharmacy i2mo, 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 

Salkowski's Physiological and Pathological Chemistry. (Orndorff.) 8vo, 

Schimpf's Text-book of Volumetric Analysis i2mo, 

Essentials of Volumetric Analysis i2mo, 

* Qualitative Chemical Analysis 8vo, 

Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 

Handbook for Cane Sugar Manufacturers i6mo, morocco, 

Stockbridge's Rocks and Soils 8vo, 

* Tillman's Elementary Lessons in Heat 8vo, 

* Descriptive General Chemistry ' 8vo, 

Treadwell's Qualitative Analysis. (Hall.) 8vo, 

Quantitative Analysis. (Hall.) 8vo, 

Turneaure and Russell's Public Water-supplies 8vo, 

Van Deventer's Physical Chemistry for Beginners. (Boltwood.) i2mo, 

* Walke's Lectures on Explosives » 8vo, 

Ware's Beet-sugar Manufacture and Refining Small 8vo, cloth, 

Washington's Manual of the Chemical Analysis of Rocks 8vo, 

Wassermann's Immune Sera : Haemolysins, Cytotoxins, and Precipitins. (Bol- 
duan.) i2mo, 

Wells's Laboratory Guide in Qualitative Chemical Analysis, 8vo, 

Short Course in Inorganic Qualitative Chemical Analysis for Engineering 

Students i2mo, 

Text-book of Chemical Arithmetic i2mo, 

Whipple's Microscopy of Drinking-water 8vo, 

Wilson's Cyanide Processes i2mo, 

Chlorirjation Process i2mo, 

Winton's Microscopy of Vegetable Foods 8vo, 

Wulling's Elementary Course in Inorganic, Rharmaceutical, and Medical 
Chemistry i2mo, 

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CIVIL ENGINEERING. 



BRIDGES AND ROOFS 



HYDRAULICS. MATERIALS OF ENGINEERING. 
RAILWAY ENGINEERING. 



Baker's Engineers' Surveying Instruments nmo, 

Bixby's Graphical Computing Table Paper ig£X 24! inches. 

** Burr's Ancient and Modern Engineering and the Isthmian Cana .. (Postage, 

27 cents additional.). 8vo, 

Comstock's Field Astronomy for Engineers. 8vo, 

Davis's Elevation and Stadia Tables 8vo, 

Elliott's Engineering for Land Drainage i2mo, 

Practical Farm Drainage i2mo, 

*Fiebeger's Treatise on Civil Engineering 8vo, 

Flemer's Phototopographic Methods and Instruments 8vo, 

Folwell's Sewerage. (Designing and Maintenance.). ..:.... 8vo, 

Freitag's Architectural Engineering. 2d Edition, Rewritten 8vo, 

French and Ives's Stereotomy 8vo, 

Goodhue's Municipal Improvements nmo, 

Goodrich's Economic Disposal of Towns' Refuse 8vo, 

Gore's Elements of Geodesy 8vo, 

Hayford's Text-book of Geodetic Astronomy 8vo, 

Hering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 

Howe's Retaining Walls for Earth nmo, 

Johnson's (J. B.) Theory and Practice of Surveying Small 8vo, 

Johnson's (L. J.) Statics by Algebraic and Graphic Methods 8vo, 

Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) . i2mo, 
Mahan's Treatise on Civil Engineering. (1873.) (Wood.) 8vo, 

* Descriptive Geometry 8vo, 

Merriman's Elements of Precise Surveying and Geodesy 8vo, 

Merriman and Brooks's Handbook for Surveyors i6mo, morocco, 

Nugent's Plane Surveying 8vo, 

Ogden's Sewer Design i2mo, 

Patton's Treatise on Civil Engineering 8vo half leather, 

Reed's Topographical Drawing and Sketching 4*0, 

Rideal's Sewage and the Bacterial Purification of Sewage .8vo, 

Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, 

Smith's Manual of Topographical Drawing. (McMillan. "> 8vo, 

Sondericker's Graphic Statics, with Applications to Trusses, Beams, and Arches. 

8vo, 
Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 

* Trautwire's Civil Engineer's Pocket-book i6mo, morocco, 

bait's Engineering and Archi'ectural Jurisprudence 8vo, 

Sheep, 
Law of Operations Preliminary (0 Construction in Engineering and Archi- 
tecture 8vo, 

Sheep, 

Law of Contracts 8vo, 

Warren's Stereotomy — Problems in Stone-cutting 8vo, 

Webb's Problems in the Use and Adjustment of Engineering Instruments. 

i6mo, morocco, 

Wilson's Topographic Surveying 8v0, 



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BRIDGES /ND ROOFS. 



Boiler's Practical Treatise on the Construction of Iron Highway Bridges. .8vo, 2 00 

* Thames River Bridge " 4to, paper, 5 00 

Burr's Course on the Stresses in Bridges and Roof Trusses, Arched Ribs, and 

Suspension Bridges. . . 8vo, 3 50 

6 



Burr and Falk's Influence Lines for Bridge and Roof Computations. . . 8vo, 3 00 

Design and Construction of Metallic Bridges 8vo, 5 00 

Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 00 

Foster's Treatise on Wooden Trestle Bridges 4to, 5 00 

Fowler's Ordinary Foundations 8vo, 3 50 

Greene's Roof Trusses 8vo, 1 25 

Bridge Trusses 8vo, 2 50 

Arches in Wood, Iron, and Stone 8vo, 2 50 

Howe's Treatise on Arches 8vo, 4 00 

Design of Simple Roof-trusses in Wood and Steel 8vo, 2 00 

Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of 

Modern Framed Structures Small 4to, 10 00 

Mtrriman and Jacoby's Text-book on Roofs and Bridges : 

Part I. Stresses in Simple Trusses 8vo, 2 50 

Part II. Graphic Statics 8vo, 2 50 

Part III. Bridge Design 8vo, 2 50 

Part IV. Higher Structures 8vo, 2 50 

Morison's Memphis Bridge 410, 10 00 

Waddell's De Pontibus, a Pocket-book for Bridge Engineers. . i6mo, morocco, 2 oo- 

♦Specifications for Steel Bridges i2mo, 5a 

Wright's Designing of Draw-spans. Two parts in one volume 8vo, 3 5a 



HYDRAULICS. 

Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from 

an Orifice. (Trautwine.) 8vo, 2 oa 

Bovey's Treatise on Hydraulics 8vo, 5 00 

Church's Mechanics of Engineering 8vo, 6 00 

Diagrams of Mean Velocity of Water in Open Channels paper, 1 50 

Hydraulic Motors 8vo, 2 00 

Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50 

Flather's Dynamometers, and the Measurement of Power i2mo, 3 00 

Folwell's Water-supply Engineering 8vo, 4 00 

Frizell's Water-power 8vo, 5 00 

Fuertes's Water and Public Health .• i2mo, 1 50 

Water-filtration Works. nmo, 2 50 

Ganguillet and Kutter's General Formula for the Uniform Flow of Water in 

Rivers and Other Channels. (Hering and Trautwine.) 8vo, 4 00 

Hazen's Filtration of Public Water-supply 8vo, 3 00 

Hazlehurst's Towers and Tanks for Water-works 8vo, 2 50 

Herschel's 115 Experiments on the Carrying Capacity of Large. Riveted, Metal 

Conduits 8vo, 2 00 

Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 

8vo, 4 00 

Merriman's Treatise on Hydraulics 8vo, 5 00 

* Michie's Elements of Analytical Mechanics 8vo, 4 00 

Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water- 
supply Large 8vo, 5 00 

** Thomas and Watt's Improvement of Rivers. (Post, 44c. additional. ).4to, 6 00 

Turneaure and Russell's Public Water-supplies 8vo, 5 00 

Wegmann's Design and Construction of Dams 4to, 5 00 

Water-supply of the City of New York from 1658 to 1895 4to, 10 00 

Williams and Hazen's Hydraulic Tables 8vo, 1 50 

Wilson's Irrigation Engineering Small 8vo, 4 00 

Wolff's Windmill as a Prime Mover 8vo, 3 00 

Wood's Turbines 8vo, 2 50 

Elements of Analytical Mechanics 8vo, 3 00 

7 



MATERIALS OF ENGINEERING. 

Baker's Treatise on Masonry Construction 8vo, 

Roads and Pavements 8vo, 

Black's United States Public Works Oblong 4*0, 

* Bovey's Strength of Materials and Theory of Structures 8vo, 

Burr's Elasticity and Resistance of the Materials of Engineering 8vo, 

Byrne's Highway Construction 8vo, 

Inspection of the Materials and Workmanship Employed in Construction. 

i6mo, 

Church's Mechanics of Engineering 8vo, 

Du Bois's Mechanics of Engineering. Vol. I Small 4to, 

*Eckel's Cements, Limes, and Plasters 8vo, 

Johnson's Materials of Construction Large 8vo, 

Fowler's Ordinary Foundations 8vo, 

* Greene's Structural Mechanics 8vo, 

Keep's Cast Iron 8vo, 

Lanza's Applied Mechanics 8vo, 

Marten's Handbook on Testing Materials. (Henning.) 2 vols 8vo f 

Maurer's Technical Mechanics 8vo, 

Merrill's Stones for Building and Decoration 8vo, 

Merriman's Mechanics of Materials 8vo, 

Strength of Materials i2mo, 

Metcalf's Steel. A Manual for Steel-users i2mo, 

Patton's Practical Treatise on Foundations 8vo, 

Richardson's Modern Asphalt Pavements 8vo, 

Richey's Handbook for Superintendents of Construction i6mo, mor., 

Rockwell's Roads and Pavements in France i2mo, 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 

Smith's Materials of Machines nmo, 

Snow's Principal Species of Wood 8vo, 

Spalding's Hydraulic Cement 121H0, 

Text-book on Roads and Pavements nmo, 

Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 

Thurston's Materials of Engineering. 3 Parts Svo, 

Part I. Non-metallic Materials of Engineering and Metallurgy 8vo, 

Part II. Iron and Steel 8vo, 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 8vo, 

Thurston's Text-book of the Materials of Construction 8vo, 

Tillson's Street Pavements and Paving. Materials 8vo, 

Waddell's De Pontibus. (A P©cket-book for Bridge Engineers.) . . i6mo, m®r., 

Specifications for Steel Bridges i2mo, 

Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on 

the Preservation of Timber 8vo, 

Wood's (De V.) Elements of Analytical Mechanics 8vo, 

Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 
Steel 8vo, 



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RAILWAY ENGINEERING. 

Andrew's Handbook for Street Railway Engineers.. .. .3x5 inches, morocco, 1 25 

Berg's Buildings and Structures of American Railroads 4to, 5 00 

Brook's Handbook of Street Railroad Location i6mo, morocco, 1 50 

Butt's Civil Engineer's Field-book i6mo, morocco, 2 50 

Crandall's Transition Curve i6mo, morocco, 1 50 

Railway and Other Earthwork Tables 8vo, 1 50 

Dawson's "Engineering" and Electric Traction Pocket-book. . i6mo, morocco, 5 00 

8 



Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 00 

* Drinker's Tunnelling, Explosive Compounds, and Rock Drills. 4to, half mor., 25 00 

Fisher's Table of Cubic Yards Cardboard, 23 

Godwin's Raiiroad Engineers' Field-book and Explorers' Guide. . . i6mo, mor., 2 50 

Howard's Transition Curve Field-book i6mo, morocco, 1 50 

Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- 
bankments 8vo, 1 00 

Molitor and Beard's Manual for Resident Engineers i6mo, 1 00 

Uagle's Field Manual for Railroad Engineers. .' i6mo, morocco, 3 00 

Philbrick's Field Manual for Engineers i6mo, morocco, 3 00 

Searles's Field Engineering i6mo, morocco, 3 00 

Railroad Spiral i6mo, morocco, 1 50 

Taylor's Prismoidal Formulae and Earthwork 8vo, 1 50 

* Trautwine's Method of Calculating the Cube Contents of Excavations and 

Embankments by the Aid of Diagrams 8vo, 2 00 

The Field Practice of Laying Out Circular Curves for Railroads. 

i2mo, morocco, 2 50 

Cross-section Sheet Paper, 25 

Webb's Railroad Construction. . i6mo, morocco, 5 00 

Wellington's Economic Theory of the Location of Railways Small 8vo, 5 00 



DRAWING. 

Barr's Kinematics of Machinery 8vo, 

* Bartlett's Mechanical Drawing 8vo, 

* " " " Abridged Ed 8vo, 

Coolidge's Manual of Drawing 8vo, paper 

Coolidge and Freeman's Elements of General Drafting for Mechanical Engi- 
neers Oblong 4to, 

Durley's Kinematics of Machines 8vo, 

Emch's Introduction to Projective Geometry and its Applications 8vo, 

Hill's Text-book on Shades and Shadows, and Perspective 8vo, 

Jamison's Elements of Mechanical Drawing 8vo, 

Advanced Mechanical Drawing 8vo, 

Jones's Machine Design: 

Part I. Kinematics of Machinery 8vo, 

Part H. Form, Strength, and Proportions of Parts 8vo, 

MacCord's Elements of Descriptive Geometry 8vo, 

Kinematics; or, Practical Mechanism 8vo, 

Mechanical Drawing 4to, 

Velocity Diagrams 8vo, 

MacLeod's Descriptive Geometry Small 8vo, 

* Mahan's Descriptive Geometry and Stone-cutting. 8vo, 

Industrial Drawing. (Thompson.) 8vo, 

Moyer's Descriptive Geometry gvo, 

Reed's Topographical Drawing and Sketching 4to, 

Reid's Course in Mechanical Drawing 8vo, 

Text-book «f Mechanical Drawing and Elementary Machine Design. 8vo, 

Robinson's Principles of Mechanism .8vo, 

Schwamb and Merrill's Elements of Mechanism 8vo, 

Smith's (R. S.) Manual of Topographical Drawing. (McMillan.) 8vo, 

Smith (A. W.) and Marx's Machine Design .8vo, 

Warren's Elements of Plane and Solid Free-hand Geometrical Drawing. i2mo, 

Drafting Instruments and Operations i2mo, 

Manual of Elementary Projection Drawing i2mo, 

Manual of Elementary Problems in the Linear Perspective of Form and 

Shadow i2mo, 

Plane Problems in Elementary Geometry i2mo, 

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Warren's Primary Geometry nmo, 75 

Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 

General Problems of Shades and Shadows 8vo, 3 00 

Elements of Machine Construction and Drawing , 8vo, 7 50 

Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 50 

Weisbach's Kinematics [and Power of Transmission. (Hermann and 

Klein.). . 8vo, 

Whelpley's Practical Instruction in the Art of Letter Engraving 12 mo, 

Wilson's (H. M.) Topographic Surveying 8vo, 

Wilson's (V. T.) Free-hand Perspective 8vo, 

Wilson's (V. T.) Free-hand Lettering 8vo, 

Woolf's Elementary Course in Descriptive Geometry Large 8vo, 

ELECTRICITY AND PHYSICS. 

Anthony and Brackett's Text-book of Physics. (Magie.) Small 8vo, 

Anthony's Lecture-notes on the Theory of Electrical Measurements. . . . i2mo, 
Benjamin's History of Electricity 8vo, 

Voltaic Cell 8vo, 

Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).8vo, 

Crehore and Squier's Polarizing Photo-chronograph 8vo, 

Dawson's "Engineering" and Electric Traction Pocket-book. i6mo, morocco, 
Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von 

Ende.) nmo, 

Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 

Flather's Dynamometers, and the Measurement of Power nmo, 

Gilbert's De Magnete. (Mottelay.) 8vo, 

Hanchett's Alternating Currents Explained nmo, 

Hering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 

Holman's Precision of Measurements 8vo, 

Telescopic Mirror-scale Method, Adjustments, and Tests. . . .Large 8vo, 

Xinzbrunner's Testing of Continuous-current Machines. . 8vo, 

Landauer's Spectrum Analysis. (Tingle.) 8vo, 

Le Chatelier s High-temperature Measurements. (Boudouard — Burgess.) nmo, 
Lob's Electrochemistry of Organic Compounds. (Lorenz.) 8vo, 

* Lyons'? Treatise on Electromagnetic Phenomena. Vols. I. and II. 8vo, each, 

* Michie's Elements of Wave Motion Relating to Sound and Light 8vo, 

Niaudet's Elementary Treatise on Electric Batteries. (Fishback.) nmo, 

* Rosenberg's Electrical Engineering. (Haldane Gee — Kinzbrunner.). . .8vo, 

Ryan, Norris, and Hoxie's Electrical Machinery. VoL 1 8vo, 

Thurston's Stationary Steam-engines 8vo, 

* Tillman's Elementary Lessons in Heat 8vo, 

Tory and Pitcher's Manual of Laboratory Physics Small 8vo, 

Ulke's Modern Electrolytic Copper Refining 8vo, 

LAW. 

* Davis's Elements of Law 8vo, 2 50 

* Treatise on the Military Law of United States 8vo, 7 00 

* ' Sheep, 7 50 

Manual for Courts-martial i6mo, morocco, 1 50 

Wait's Engineering and Architectural Jurisprudence 8vo, 6 00 

Sheep, 6 50 
Law of Operations Preliminary to Construction in Engineering and Archi- 
tecture 8vo 5 00 

Sheep, 5 50 

Law of Contracts 8vo, 3 00 

Winthrop's Abridgment of Military Law nmo. 2 50 

10 



MANUFACTURES. 

Bernadou's Smokeless Powder — Nitro-cellulose and Theory of the Cellulose 

Molecule i2mo, 2 50 

Bolland's Iron Founder nmo, 2 50 

"The Iron Founder," Supplement i2mo, 2 50 

Encyclopedia of Founding and Dictionary of Foundry Terms Used in the 

Practice of Moulding nmo, 3 00 

* Eckel's Cements, Limes, and.Plasters 8vo, 6 00 

Eissler's Modern High Explosives -. . . .8vo, 4 00 

Effront's Enzymes and their Applications. (Prescott.) 8vo, 3 00 

Fitzgerald's Boston Machinist i2mo, 1 00 

Ford's Boiler Making for Boiler Makers i8mo, 1 00 

Hopkin's Oil-chemists' Handbook 8vo, 3 00 

Keep's Cast Iron , 8vo, 2 50 

Leach's The Inspection and Analysis of Food with Special Reference to State 

Control Large 8vo, 7 50 

* McKay and Larsen's Principles and Practice of Butter-making 8vo, 1 50 

Matthews's The Textile Fibres 8vo, 3 50 

Metcalf 's Steel. A Manual for Steel-users . nmo, 2 00 

Metcalfe's Cost of Manufactures — And the Administration of Workshops. 8vo, 5 00 

Meyer's Modern Locomotive Construction 4to, 10 00 

Morse's Calculations used in Cane-sugar Factories i6mo, morocco, 1 50 

* Reisig's Guide to Piece-dyeing 8vo, 25 00 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00 

Smith's Press-working of Metals 8vo, 3 00 

Spalding's Hydraulic Cement nmo, 2 00 

Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 3 00 

Handbook for Cane Sugar Manufacturers i6mo, morocco, 3 00 

Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 00 

Thurston's Manual of Steam-boilers, their Designs, Construction and Opera- 
tion 8vo, 5 00 

* Walke's Lectures on Explosives 8vo, 4 00 

Ware's Beet-sugar Manufacture and Refining Small 8vo, 4 00 

West's American Foundry Practice nmo, 2 50 

Moulder's Text-book nmo, 2 50 

Wolff's Windmill as a Prime Mover 8vo, 3 00 

Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. .8vo, 4 00 

MATHEMATICS. 

Baker's Elliptic Functions 8vo, 

* Bass's Elements of Differential Calculus nmo, 

Briggs's Elements of Plane Analytic Geometry nmo, 

Compton's Manual of Logarithmic Computations nmo, 

Davis's Introduction to the Logic of Algebra 8vo, 

* Dickson's College Algebra Large nmo, 

* Introduction to the Theory of Algebraic Equations Large nmo, 

Emch's Introduction to Projective Geometry and its Applications 8vo, 

Halsted's Elements of Geometry , . .8vo, 

Elementary Synthetic Geometry 8vo, 

Rational Geometry nmo, 

* Johnson's (J. B.) Three-place Logarithmic Tables: Vest-pocket size. paper, 

100 copies for 

* Mounted on heavy cardboard, 8X 10 inches, 

10 copies for 
Johnson's (W. W.) Elementary Treatise on Differential Calculus . Small 8vo, 

Elementary Treatise on the Integral Calculus Small 8vo, 

11 



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Johnson's (W. W.) Curve Tracing in Cartesian Co-ordinates • nmo, i oo 

Johmson's (W. W.) Treatise on Ordinary and Partial Differential Equations. 

Small 8vo, 3 50 
Johnson's (W. W.) Theory of Errors and the Method of Least Squares, nmo, 1 50 

* Johnson's (W. W.) Theoretical Mechanics i2mo, 3 00 

Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.). 12 mo, 2 00 

* Ludlow and Bass. Elements of TrigoMometry and Logarithmic and Other 

Tables , 8vo, 3 00 

Trigonometry and Tables published separately Each, 2 00 

* Ludlow's Logarithmic and Trigonometric Tables 8vo, 1 00 

Mathematical Monographs. Edited by Mansfield Merriman and Robert 

S. Woodward Octavo, each 1 00 

No. 1. History of Modern Mathematics, by David Eugene Smith. 
No. 2. Synthetic Projective Geometry, by George Bruce Halsted. 
No. 3. Determinants, by Laenas Gifford Weld. No. 4. Hyper- 
bolic Functions, by James McMahon. No. 5. Harmonic Func- 
tions, by William E. Byerly. No. 6. Grassmann's Space Analysis, 
by Edward W. Hyde. No. 7. Probability and Theory of Errors, 
by Robert S. Woodward. No. 8. Vector Analysis and Quaternions, 
by Alexander Macfarlane. No. 9. Differential Equations, by 
William Woolsey Johnson. No. 10. The Solution of Equations, 
by] Mansfield Merriman. No. 11. Functions of a Complex Variable, 
by Thomas S. Fiske. 

Maurer's Technical Mechanics 8vo, 4 00 

Merriman's Method of Least Squares 8vo, 2 00 

Rice and Johnson's Elementary Treatise on the Differential Calculus. . Sm. 8vo, 3 00 

Differential and Integral Calculus. 2 vols, in one Small 8vo, 2 50 

Wood's Elements of Co-ordinate Geometry 8vo, 2 00 

Trigonometry: Analytical, Plane, and Spherical i2mo, 1 00 



MECHANICAL ENGINEERING. 



MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS. 

Bacon's Forge Practice i2mo, 

Baldwin's Steam Heating for Buildings i2mo, 

Barr's Kinematics of Machinery 8vo, 

* Bartlett's Mechanical Drawing 8vo, 

* " " " Abridged Ed . .8vo, 

Benjamin's Wrinkles and Recipes nmo, 

Carpenter's Experimental Engineering 8vo, 

Heating and Ventilating Buildings 8vo, 

Cary's Smoke Suppression in Plants using Bituminous Coal. (In Prepara- 
tion.) 

Clerk's Gas and Oil Engine Small 8vo, 

Coolidge's Manual of Drawing 8vo, paper, 

Coolidge and Freeman's Elements of General Drafting for Mechanical En- 
gineers Oblong 4to, 

Cromwell's Treatise on Toothed Gearing. iamo, 

Treatise on Belts and Pulleys nmo, 

Durley's Kinematics of Machines 8vo, 

Flather's Dynamometers and the Measurement of Power nmo, 

Rope Driving i2mo, 

Gill's Gas and Fuel Analysis for Engineers nmo, 

Hall's Car Lubrication nmo, 

Hering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 

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Hutton's The Gas Engine 8vo, 

Jamison's Mechanical Drawing 8vo, 

Jones's Machine Design: 

Part I. Kinematics of Machinery. 8vo, 

Part II. Form, Strength, and Proportions of Parts 8vo, 

Kent's Mechanical Engineers' Pocket-book i6mo, morecco, 

Kerr's Power and Power Transmission 8vo, 

Leonard's Machine Shop, Tools, and Methods 8vo, 

* Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean. ) . . 8vo, 
MacCord's Kinematics; or, Practical Mechanism . .8vo, 

Mechanical Drawing 4*0, 

Velocity Diagrams 8vo, 

MacFarland's Standard Reduction Factors for Gases 8vo, 

Mahan's Industrial Drawing. (Thompson.) 8vo, 

Poole's Calorific Power of Fuels 8vo, 

Reid's Course in Mechanical Drawing 8vo, 

Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 

Richard's Compressed Air nmo, 

Robinson's Principles of Mechanism 8vo, 

Schwamb and Merrill's Elements of Mechanism 8vo, 

Smith's (O.) Press- working of Metals 8vo, 

Smith (A. W.) and Marx's Machine Design 8vo, 

Thurston's Treatise on Friction and Lost Work in Machinery and Mill 
Work 8vo, 

Animal as a Machine and Prime Motor, and the Laws of Energetics. i2mo, 

Warren's Elements of Machine Construction and Drawing 8vo, 

Weisbach's Kinematics and the Power of Transmission. (Herrmann — 
Klein.) 8vo, 

Machinery of Transmission and Governors. (Herrmann — Klein.). .8vo, 

Wolff's Windmill as a Prime Mover 8vo, 

Wood's Turbines. . , , 8vo, 



MATERIALS OP ENGINEERING. 

* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 

Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition. 

Reset 8vo, 

Church's Mechanics of Engineering '. 8vo, 

* Greene's Structural Mechanics 8vo, 

Johnson's Materials of Construction 8vo, 

Keep's Cast Iron 8vo, 

Lanza's Applied Mechanics 8vo, 

Martens's Handbook on Testing Materials. (Henning.) 8vo, 

Maurer's Technical Mechanics 8vo, 

Merriman's Mechanics of Materials 8vo, 

Strength of Materials nmo, 

Metcalf's Steel. A manual for Steel-users izmo, 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 

Smith's Materials of Machines t i2mo, 

Thurston's Materials of Engineering 3 vols., 8vo, 

Part II. Iron and Steel 8vo, 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 8vo, 

Text-book of the Materials of Construction 8vo, 

Wood's (De V.) Treatise on the Resistance of Materials and an Appendix on 

the Preservation of Timber 8vo, 

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Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 00 

Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 

Steel 8vo : 4 00 

STEAM-ENGINES AND BOILERS. 

Berry's Temperature-entropy Diagram i2mo, 1 25 

Carnot's Reflections on the Motive Power of 'Heat. (Thurston.). .... .i2mo, 1 50 

Dawson's "Engineering" and Electric Traction Pocket-book. . . .i6mo, mor., 5 00 

Ford's Boiler Making for Boiler Makers. i8mo, 1 00 

Goss's Locomotive Sparks 8vo, 2 00 

Hemenway's Indicator Practice and Steam-engine Economy i2mo, 2 00 

Hutton's Mechanical Engineering of Power Plants 8vo, 5 00 

Heat and Heat-engines 8vo, 5 00 

Kent's Steam boiler Economy 8vo, 4 00 

Kneass's Practice and Theory of the Injector 8vo, 1 50 

MacCord's Slide-valves 8vo, 2 00 

Meyer's Modern Locomotive Construction 4to, 10 oc 

Peabody's Manual of the Steam-engine Indicator nmo, 1 50 

Tables of the Properties of Saturated Steam and Other Vapors 8vo, 1 00 

Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 00 

Valve-gears for Steam-engines 8vo, 2 50 

Peabody and Miller's Steam-boilers 8vo, 4 00 

Pray's Twenty Years with the Indicator Large 8vo, 2 50 

Pupin's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors. 

(Osterberg.) i2mo, 1 25 

Reagan's Locomotives : Simple Compound, and Electric i2mo, 2 50 

Rontgen's Principles of Thermodynamics. (Du Bois.) 8vo, 5 00 

Sinclair's Locomotive Engine Running and Management i2mo, 2 00 

Smart's Handbook of Engineering Laboratory Practice i2mo, 2 50 

Snow's Steam-boiler Practice 8vo, 3 00 

Spangler's Valve-gears 8vo, 2 50 

Notes on Thermodynamics i2mo, 1 00 

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 00 

Thomas's Steam-turbines 8vo, 3 50 

Thurston's Handy Tables 8vo, 1 50 

Manual of the Steam-engine 2 vols., 8vo, 10 00 

Part I. History, Structure, and Theory 8vo, 6 00 

Part II. Design, Construction, and Operation 8vo, 6 00 

Handbook of Engine and Boiler Trials, and the Use of the Indicator and 

the Prony Brake 8vo, 5 00 

Stationary Steam-engines 8vo, 2 50 

Steam-boiler Explosions in Theory and in Practice i2mo, 1 50 

Manual of Steam-boilers, their Designs, Construction, and Operation 8vo, 5 00 

Weisbach's Heat, Steam, and Steam-engines. (Du Bois.) 8vo, 5 00 

Whitham's Steam-engine Design 8vo, 5 00 

Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .8vo, 4 00 






MECHANICS AND MACHINERY. 

Barr's Kinematics of, Machinery 8vo, 2 50 

*,Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 

Chase's The Art of Pattern-making i2mo, 2 50 

Church's Mechanics of Engineering 8vo, 6 00 

Notes and Examples in Mechanics 8vo, 2 00 

Compton's First Lessons in Metal-working i2mo, 1 5° 

Compton and De Groodt's The Speed Lathe i2mo 1 50 

14 



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Cromwell's Treatise on Toothed Gearing i2mo. 

Treatise on Belts and Pulleys i2mo> - so 

Dana's Text-book of Elementary Mechanics for Colleges and Schools. . nmo, i 50 

Dingey's Machinery Pattern Making i2mo, 2 00 

Dredge's Record of the Transportation Exhibits Building of the World's 

Columbian Exposition of 1893 4to half morocco, 5 00 

Du Bois's Elementary Principles of Mechanics : 

Vol. I. Kinematics 8vo, 3 50 

Vol. II. Statics 8vo, 4 00 

Mechanics of Engineering. Vol. I Small 4to, 7 50 

Vol. II Small 4to, 10 00 

Durley's Kinematics of Machines , 8vo, 4 00 

Fitzgerald's Boston Machinist i6mo, 1 00 

Flather's Dynamometers, and the Measurement of Power nmo, 3 00 

Rope Driving i2mo, 2 00 

Goss's Locomotive Sparks 8vo, 2 00 

* Greene's Structural Mechanics 8vo, 2 50 

Hall's Car Lubrication i2mo, 1 00 

Holly's Art of Saw Filing . i8mo, 75 

James's Kinematics of a Point and the Rational Mechanics of a Particle. 

Small 8vo, 2 00 

* Johnson's (W. W.) Theoretical Mechanics i2mo, 3 00 

Johnson's (L. J.) Statics by Graphic and Algebraic Methods. . . , 8vo, 2 00 

Jones's Machine Design: 

Part I. Kinematics of Machinery 8vo, 1 50 

Part II. Form, Strength, and Proportions of Parts 8vo, 3 00 

Kerr's Power and Power Transmission 8vo, 2 00 

Lanza's Applied Mechanics 8vo, 7 50 

Leonard's Machine Shop, Tools, and Methods 8vo, 4 00 

* Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.). 8vo, 4 00 
MacCord's Kinematics; or, Practical Mechanism : .8vo, 5 00 

Velocity Diagrams 8vo, 1 50 

Maurer's Technical Mechanics 8vo, 4 00 

Merriman's Mechanics of Materials 8vo, 5 00 

* Elements of Mechanics nmo, 1 00 

* Michie's Elements of Analytical Mechanics 8vo, 4 00 

Reagan's Locomotives: Simple, Compound, and Electric nmo, 2 50 

Reid's Course in Mechanical Drawing 8vo, 2 00 

Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 00 

Richards's Compressed Air nmo, 1 50 

Robinson's Principles of Mechanism 8vo, 3 00 

Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 

Schwamb and Merrill's Elements of Mechanism 8vo, 3 co 

Sinclair's Locomotive-engine Running and Management nmo, 2 00 

Smith's (O.) Press-working of Metals 8vo, 3 00 

Smith's (A. W.) Materials of Machines nmo, 1 00 

Smith (A. W.) and Marx's Machine Design 8vo, 3 00 

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 00 

Thurston's Treatise on Friction and Lost Work in Machinery and Mill 

Work 8vo, 3 00 

Animal as a Machine and Prime Motor, and the Laws of Energetics. 

nmo, 1 00 

Warren's. Elements of Machine Construction and Drawing 8vo, 7 50 

Weisbach's Kinematics and Power of Transmission. ( Herrmann — Klein. ) . 8vo , 5 00 

Machinery of Transmission and Governors. (Herrmann — Klein. ).8vo, 5 00 
Wood's Elements of Analytical Mechanics 8vo, 3 00 

Principles of Elementary Mechanics nmo, 1 25 

Turbines 8vo, 2 50 

The World's Columbian Exposition of 1893 ... .• 4to, 1 00 

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METALLURGY. 






Egleston's Metallurgy of Silver, Gold, and Mercury: 

Vol. I. Silver 8vo, 

Vol. II. Gold and Mercury 8vo, 

** Iles's Lead-smelting. (Postage 9 cents additional.) i2mo, 

Keep's Cast Iron 8vo, 

Kunhardt's Practice of Ore Dressing in Europe 8vo, 

Le Chatelier's High-temperature Measurements. (Boudouard — Burgess. )nmo. 

Metcalf's Steel. A Manual for Steel-users i2mo, 

Minet's Production of Aluminum and its Industrial Use. (Waldo.). . • • i2mo, 

Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 

Smith's Materials of Machines i2mo, 

Thurston's Materials of Engineering. In Three Parts 8vo, 

Part II. Iron and Steel 8vo, 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 8vo, 

Ulke's Modern Electrolytic Copper Refining 8vo, 



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MINERALOGY. 



Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2 50 

Boyd's Resources of Southwest Virginia 8vo, 3 00 

Map of Southwest Virignia Pocket-book form. 2 00 

Brush's Manual of Determinative Mineralogy. (Penfield.). . 8vo, 4 00 

Chester's Catalogue of Minerals 8vo, paper, 1 00 

Cloth, 1 25 

Dictionary of the Names of Minerals 8vo, 3 50 

Dana's System of Mineralogy Large 8vo, half leather, 12 50 

First Appendix to Dana's New " System of Mineralogy." Large 8vo, 1 00 

Text-book of Mineralogy 8vo, 4 00 

Minerals and How to Study Them i2mo. 1 50 

Catalogue of American Localities of Minerals Large 8vo, 1 00 

Manual of Mineralogy and Petrography i2mo, 2 00 

Douglas's Untechnical Addresses on Technical Subjects i2mo, 1 00 

Eakle's Mineral Tables 8vo, 1 25 

Egleston's Catalogue of Minerals and Synonyms 8vo, 2 50 

Hussak's The Determination of Rock-forming Minerals. ( Smith.). Small 8vo, 2 00 

Merrill's Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 00 

* Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests. 

8vo, paper, 50 
Rosenbusch's Microscopical Physiography of the Rock-making Minerals. 

(Iddings.) 8vo, 5 00 

* Tillman's Text-book of Important Minerals and Rocks 8vo, 2 00 



MINING. 



Beard's Ventilation of Mines i2mo, 2 50 

Boyd's Resources of Southwest Virginia f vo, 3 00 

Map of Southwest Virginia Pocket-book form 2 00 

Douglas's Untechnical Addresses on Technical Subjects i2mo. 1 00 

* Drinker's Tunneling, Explosive Compounds, and Rocx Drills. . 4to,hf. mor., 25 00 

Eissler's Modern High Explosives 8vo, 4 00 

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Goodyear's Coal-mines of the Western Coast of the United States i2mo, 

Ihlseng's Manual of Mining 8vo, 

** Ues's Lead-smelting. (Postage ox. additional.) nmo, 

Kunhardt's Practice of Ore Dressing in Europe 8vo, 

O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 

Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 

* Walke's Lectures on Explosives 8vo, 

Wilson's Cyanide Processes nmo, 

Chlorination Process i2mo, 

Hydraulic and Placer Mining nmo, 

Treatise on Practical and Theoretical Mine Ventilation nmo, 



SANITARY SCIENCE. 

Bashore's Sanitation ®f a Country House nmo, 

Folwell's Sewerage. (Designing, Construction, and Maintenance.) 8vo, 

Water-supply Engineering 8vo, 

Fowler's Sewage Works Analyses nmo, 

Fuertes's Water and Public Health : nmo, 

Water-filtration Works. nmo, 

Gerhard's Guide to Sanitary House-inspection i6mo, 

Goodrich's Economic Disposal of Town's Refuse Demy 8vo, 

Hazen's Filtration of Public Water-supplies 8vo, 

Leach's The Inspection and Analysis of Food with Special Reference to State 

Control 8vo, 

Mason's Water-supply. (Considered principally from a Sanitary Standpoint) 8vo, 

Examination of Water. (Chemical and Bacteriological.) nmo, 

Ogden's Sewer Design nmo, 

Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- 
ence to Sanitary Water Analysis nmo, 

* Price's Handbook on Sanitation. nmo, 

Richards's Cost of Food. A Study in Dietaries nmo, 

Cost of Living as Modified by Sanitary Science nmo, 

Cost of Shelter nmo, 

Richards and Woodman's Air, Water, and Food from a Sanitary Stand- 
point 8vo, 

* Richards and Williams's The Dietary Computer 8vo, 

Rideal's Sewage and Bacterial Purification of Sewage 8vo, 

Turneaure and Russell's Public Water-supplies 8vo, 

Von Behring's Suppression of Tuberculosis. (Bclduan.) nmo, 

Whipple's Microscopy of Drinking-water .• 8vo, 

Winton's Microscopy of Vegetable Foods 8vo, 

Woodhull's Notes on Military Hygiene i6mo, 

* Personal H/giene nmo, 



MISCELLANEOUS. 

De Fursac's Manual of Psychiatry. (Rosanoff and Collins.). . . .Large nmo, 
Emmons's Geological Guide-took of the Rocky Mountain Excursion of the 

International Congress of Geologists Large £vo, 

Ferrel's Popular Treatise on the Winds 8vo 

Haines's American Railway Management nmo, 

Mott's Fallacy of the Present Theory of Sound i6mo, 

Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894. .Small 8vo, 

Rostoski's Serum Diagnosis. (Bolduan.) nmo. 

Rotherham's Emphasized New Testament Large 8vo, 

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Steel's Treatise on the Diseases of the Dog. 8ve, 3 50 

The World's Columbian Exposition of 1893 4to, 1 00 

Von Behring's Suppression of Tuberculosis. (Bolduan.) nmo, 1 00 

Winslow's Elements of Applied Microscopy : . i2mo, 1 50 

Worcester and Atkinson. Small Hospitals, Establishment and Maintenance; 

Suggestions for Hospital Architecture : Plans for Small Hospital . 1 2 mo , 125 



HEBREW AND CHALDEE TEXT-BOOKS. 



Green's Elementary Hebrew Grammar i2mo, 

Hebrew Chrestomathy 8vo, 

Gesenius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures. 

(Tregelles.) Small 4to, half morocco, 

Letteris's Hebrew Bible; 8vo, 

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